TabSDS: a Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Authors: Elias Chaibub Neto
Venue: ICML 2025 poster (2025)
Keywords: Tabular synthetic data
non-parametric
model-free
lightweight
Primary area: deep_learning->generative_models_and_autoencoders
TL;DR: TabSDS is a lightweight, non-parametric alternative to deep generative models for tabular data, offering very competitive performance, significantly faster execution, and open-source implementations in R and Python.

Abstract: The development of deep generative models for tabular data is currently a very active research area in machine learning. These models, however, tend to be computationally heavy and require careful tuning of multiple model parameters. In this paper, we propose TabSDS - a lightweight, non-parametric, and model free alternative to tabular deep generative models which leverages rank and data shuffling transformations for generating synthetic data which closely approximates the joint probability distribution of the real data. We evaluate TabSDS against multiple baselines implemented in the Synthcity Python library across several datasets. TabSDS showed very competitive performance against all baselines (including TabDDPM - a strong baseline model for tabular data generation). Importantly, the execution time of TabSDS is orders of magnitude faster than the deep generative baselines, and also considerably faster than other computationally efficient baselines such as adversarial random forests.

TabSDS: a Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Elias Chaibub Neto
Abstract
tain heterogeneous relationships among distinct data types, and usually tend be considerably smaller than the large scale datasets used to train computer vision and natural language processing tasks.
The development of deep generative models for tabular data is currently a very active research area in machine learning. These models, how- ever, tend to be computationally heavy and re- quire careful tuning of multiple model parameters. In this paper, we propose TabSDS lightweight, non-parametric, and model free alternative to tab- ular deep generative models which leverages rank and data shuffling transformations for generating synthetic data which closely approximates the joint probability distribution of the real data. We evaluate TabSDS against multiple baselines im- plemented in the Synthcity Python library across several datasets. TabSDS showed very competi- tive performance against all baselines (including TabDDPM a strong baseline model for tabular data generation). Importantly, the execution time of TabSDS is orders of magnitude faster than the deep generative baselines, and also considerably faster than other computationally efficient base- lines such as adversarial random forests.
The generation of synthetic tabular data has been research topic in the statistical disclosure control field for over three decades now (Drechsler and Haensch, 2023; Reiter, 2023). More recently, the machine learning community has also turned its attention tabular data, and several sophisticated deep generative modeling frameworks (including generative adversarial networks, variational autoencoders, diffusion models, normalizing flows, and large language models) have also been adapted for the generation of tabular data (see Bond- Bond-Taylor et al. 2021; Lu et al., 2023; Fang et al., 2024 for a few recent reviews).
These deep learning based approaches, however, tend to be computationally intensive and require extensive tuning of multiple model parameters. This caveat has motivated the development of more lightweight alternatives such as adversarial random forests (Watson et al., 2023).
In this paper, we propose a lightweight alternative to deep generative models as well. Building over sequential joint probability preserving data shuffling (SJPPDS), recently proposed perturbative method for performing statistical dis- closure control of numeric data (Chaibub Neto, 2024), we develop a completely non con-aaraettric and model free ap- proach for synthetic tabular data generation.
1. Introduction
Easy access data is fundamental for machine learning research. Real-world data, however, often contains sensi- tive information, which precludes its unrestricted sharing across the research community. As result, synthetic data has become an increasingly popular alternative for training MI. models. The goal is to create training datasets that closely resemble real-world data, allowing models trained on synthetic data to perform effectively on real data.
high level, our approach leverages rank and data shuf- fling transformations for the generation of synthetic data, It represents multi-step procedure involving the genera- tion of (uncorrelated) synthetic marginal distributions which are then rank-matched to shuffled versions of the real data. The synthetic marginal distributions are generated using a novel non- parametric approach which (in the asymptotic case) draws samples from the same distribution as the real data (see Theorem 1). The matching step essentially induces the association structure of the real data into the synthetic marginal data. The result is the generation of the synthetic data which closely approximates the joint proba- bility distribution of the real data. Our main contributions are the following.
However, generating high-quality synthetic data that accu- rately reflects the complexities of real-world data remains significant challenge for tabular datasets, which often con-
'Sage Bionetworks, Seattle, Washington, United States of America. Correspondence to: Elias Chaibub Neto wet.laa.caaiuu..eto@@@ooooo sag.bsss.ggbbbb............
Proceedings of the 4nnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

---

TabSDS: Lightweight, Fully Non-Parametric and Model Free Approach for Generating Synthetic Tabular Data
First, we introduce the synthetic tabular sequential joint probability preserving data shufflin approach, which we denote (for short) as TabSDS (Tabular Synthetic Data Shuffling) principled fully non porramamttricc and model free method for the generation of mixed synthetic data con- taining numeric and categorical variables. TabSDS extends the SJPPDS data perturbation approach in two important ways. First, it accounts for categorical variables (while SJPPDS is only applicable to numeric data). Second, it extends SJPPDS from data perturbation approach (where the data is shuffled but no new values are generated) into a fully synthetic data method. Quite importantly, TabSDS is a truly lightweight approach, being considerably faster than adversarial random forests (the current state-of-the-art for computational efficiency among the strongest baseline methods for tabular data) and is orders of magnitude faster than deep generative methods.
recently, Chaibub Neto (2024) proposed SJPPDS, a more principled data shuffling approach for numeric data, which tends to outperform CART in terms of data fidelity at the expense of a small increase in privacy risk. The TabSDS approach, proposed in this paper, extends SJPPDS (which is reviewed in the Background section) from a data pertur- bation method for numeric data into a fully blown synthetic data approach for mixed tabular data.
A synthetic data method related to TabSDS has been re- cently proposed by Domingo-Ferrer et al. (2025). Similarly to our contribution, their work is also based on the permu- tation of data ranks. But, contrary to our approach, their method is considerably more difficult to apply in practice as it: (i) requires the identification of the marginal distribu- tions of the data using predefined parametric distributions (e.g., Gaussian, Gamma, etc); and (ii) requires the use of more complex ontology-based semantic ranking approach (Domingo-Feree Ferrerr et al., 2013) for handling categorical vari- ables. Another they difference is that their method relies on different data shuffling algorithms, rather than the SJPPDS method adopted here.
Second, we show that contrary to deep generative models which require extensive tuning of multiple parameters, Tab- SDS depends more critically on a single tuning parameter which controls the amount of data shuffling. In addition to being easier to tune, this allows for a very precise control of the trade-off between data utility/fidelity and data privacy.
The number of tabular data generators in the ML literature is fairly large (see see Bond-Taylor et al. 2021; Lu et al., 2023; Fang et al., 2024 for reviews). In this paper, we com- pare TabSDS against diverse and representative selection of synthetic data generators available in Synthcity. The se- lected models included: bayesian networks ( (Young, 2009), traditional statistical method, which uses graphical models to represent probabilistic relationships; conditional tabular generative adversarial networks (CTGAN) (Xu et al., 2019), deep learning-based approach that leverages conditional GANs to model complex non-linear dependencies in tab- ular data; tabular variational autoencoders (TVAF) (Xu et al., 2019), a specialized form of variational autoencoder designed specifically for tabular data; adversarial random forests (ARF) (Watson et al., 2023), which employs a recur- sive process where trees gradually capture the data's struc- tural properties through alternating phases of generation and discrimination; and tabular denoising diffusion probabilistic models (DDPM or TabDDPM) (Kotelnikov et al., 2023), which uses a diffusion- based model specifically developed for tabular data and represents a very strong baseline model in terms of data quality. (DDPM has been highlighted as one of the strongest baselines in recent benchmarking studies (Kindji et al., 2024; Du and Li. 2025).)
Third, we benchmark TabSDS against alternative genera- tors available in the Synthcity library (Qian et al., 2023) across multiple datasets, and show that it consistently shows very competitive performance against the alternative ap- proaches (including TabDDPM one of the current state-of- the-art for data quality).
2. Related Work
Synthetic tabular data generation typically employs either machine learning or statistical models to produce artificial datasets that replicate the structure and statistical character- isties of real-world data.
Traditional synthetic data approaches based on statistical models include information preserving statistical obfusca- tion (IPSO) methods (Burridge, 2003; Cano and Torra, 2009;
Langsrud, 2019), bayesian-network methods (Young, 2009), and fully conditional specification (FCS) methods (Drech- sler, 1). Non non-parametric FCS methods based on CART models (Reiter, 2005) are considered state-of-the-art syn- thesizers in the statistical disclosure control (SDC) field (Drechsler and Reiter, 201 1; Nowok, 2016).
While several recently proposed generators have improved upon DDPM (Jolicoeur-Martinall et al., 2024; Zhang et al., 2024; Shi et al. 2025; Cresswell and Kim, 2024), none of these methods are available in Syntheity. Furthermore, the evaluations presented in these recent works consistently place DDPM among the top generators across numerous evaluation metrics (with DDPM often ranking in second
In addition to synthetic data, the SDC literature is rich with data perturbation methodology (which attempts to preserve privacy by perturbing the data, rather than synthesizing new datasets from scratch). Traditional perturbative methods include microaggregation (Domingo-Ferreer al., 2002), noise addition (Brand, 2004), rank-swapping (Moore, 1996), and data shufiling (Muralidhar and Sarathy, 2006). More
2

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
place, only behind the proposed method). Finally, it is im- portant to point out that all these additional models still re- quire extensive optimization and are computationally more expensive than TabSDS
the X₃ data within each level of the C2 variable, as shown in the X row of Table 1. Contrary the standard permuta- tions which completely destroys the association between X and X₂ (Figure lc), the restricted permutation procedure preserves the association to a good extent (Figure 1b). Note that the number of categories/levels, Thes can be used to tune the amount of shuffling of the X, variable, with larger ne values leading to less overall shuffling and better association preservation between X and X2-
3. BBckkround the SJPPDS Approach
Recently Chaibub Neto (2024) proposed the sequential joint probability preserving data shuffling (SJPPDS) approach, as more principled data perturbation method for statistical disclosure control of numeric microdata. Traditional data perturbation approaches (e.g., microaggregatiin) tend to be "ad-hoc" in the sense that while they preserve some particular aspects of the data, they end up modifying others.
The SJPPDS algorithm corresponds, essentially, to repeated applications of restricted permutations to the first p - 1 columns of a numerical dataset relative to its last column, over sequential rearrangements of the order of the columns. For instance, for dataset containing p p= 3 variables the algorithm performs a restricted permutation of { X2} relative to X3, then of {X2, Xs} relative to X1, and finally of [X3, X1} relative to X²- For completeness, the SJPPDS procedure is presented in Algorithm 6 in the Appendix. (See also Chaibub Neto 2024 for more details.)
The basic idea behind the SJPPDS approach is to approx- imate the joint distribution of the real (numeric) data via sequential applications of restricted permutations to the data (where the restricted permutations are guided by the joint distribution of a discretized version of the data). Importantly, because the approach only shuffles the data, the marginal dis- tributions of the perturbed data are identical to the marginal distributions of the real data. The main drawbacks of SJP- PDS that it is only applicable to numeric data, and is unable to generate new data values (it only shuffles the data).
4. The TabSDS Approach
TabSDS extends SJPPDS to categorical and synthetic data by leveraging rank transformations.
To explain how restricted permutations generate shuffled data which still retains the statistical association structure of the real data, we closely follow the illustrative example Chaibub Neto (2024). Consider a
As described in Algorithm 1, the TabSDS approach calls 3 distinct algorithms depending on whether the data con- tains: (i) only numeric variables (lines and 3 of Algorithm I); only categorical variables (lines 5 and 6); or (iii) both numeric and categorical variables (lines and 9).
provided in Section toy dataset composed of two correlated variables, X1 and X2, shown in rows 1 and 2 of Table and in Figure la
Algorithm TabSDS(X, in. les Ply p)
I: Input: data matrix X; indexes of the numeric variables
Table 1. Restricted permutation toy example
X1
8.8
9.5
9.3
9.7
10.9
9.6
10.2
11.4
12.1
ini indexes of the categorical variables ic; number of levels nı; sampling proportion p
X2
9.6
10.1
10.5
10.8
11.1
11.4
11.6
11.9
12.2
C2
a
a
a
b
b
0
c
if X contains only numeric data then
X
9.3
8.8
9.5
10.9
9.7
9.6
12.1
10.2
11.4
3: X, < SyytheticSSJPPDSSXXX (X, ne.
4: end if
oriainal data
restricted pormutation
standard permutation
5: if X contains only categorical data then
120
Dei uit cbr 00 besaont C DCcoeoan
(a)
(b)
(C)
6: X, + -CategoricalSJPPDS/ X, n.)
110
cut 06 TON S. Marer
7: end if
x.3
180
if X contains numerical and categorical data then
X, < MixxdSSytheiieSSPPSSSXX in dey Re: p)
10: end if
10.5
11: Output: synthetic data X,
Figure I. Restricted permutation example.
To generate a restricted permutation of the X₁ data relative to the X2 variable we proceed as follows. First, we dis- cretize the X₂ data into n. categories to obtain the categori- cal version of X2, represented by C2 in Table 1. (The dis- cretization is done by binning the range of X2 into = 3 equally sized buckets, which are assigned categorical levels "a", "b", and "c".) A restricted permutation of X, relative to X₂ then generated by separately permuting the values of
In the next subsections we go over each of these algorithms.
4.1. The SynthetieSJPPDS Approach
The SyntheticSJPPDS approach (Algorithm 2) leverages rank and data shuffling transformations for the generation of synthetic data, At a high level, it corresponds to a two step procedure which first generates (uncorrelated) synthetic data
3

---

TabSDS: Lightweight, Fully Non- Mon-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
from the same marginal distributions as the original data, followed by a rank-matching operation which essentially induces the association structure of the real data into the synthetic marginal data. Next we describe the algorithm in more detail.
Note that by randomly interpolating the values of order statistics in two random subsamples of the real data, Algo- rithm 3 generates synthetic data which approximates the marginal distribution as the real data. Figures 6 and 7 in the Appendix provide illustrative examples. In the asymp- totic case, where the subsample size m grows to infinity, the following result (proved in Appendix C) holds.
Algorithm 2 SyntheticSIPPDDSX. nle, p)
1: Input: numeric data matrix X; number of levels ne: sampling proportion p
and X2 (I2.1...., I2,m) represent random subsamples of size m from a random variable X distributed as X ~ Fx. Then the distribution of the synthetic data, &, generated by Algo- rithm converges almost surely to Fx as m m- oc.
Theorem 1. Let X1 = (I1,1,...,,11,.))
2: M. CGnnraaeSynhheiicMMagiiiaaSSSSSS p) {create
synthetic marginal distributions (Algoritim 8)}
3: X SJPPDS (X, ne)) [perform sequential joint probability pre-
serving data shuffling on X (Algorithm 6)
4: R <-
[create matrix of ranks from the shuffled data (tics are broken at random))
DataRank
While Theorem 1 only proves that Algorithm 3 draws synthetic samples from the same marginal distribution as the real data in the asymptotic case, in practice the pro- cedure produces very good approximations to the distri- bution of X in the finite sample setting as well. To see why, note that, by construction, for any value of t, we have that the empirical cumulative distribution func- tion (ecdf) of the interpolated synthetic sample, F is bounded by min (1), (())(()} S (1) S max Fm..a (f), Fm,,(()), where Fm,1 and Fm.2 represent the ecdfs of the x1 and x2 subsamples (as shown in Figure 8 in the Appendix). Hence, if both Pm., and Fm, provide good approximations to Fx, it also follows that f will also provide good approximation.
5: X f
MatchRanks(M,, R*)
(rank mutch the synthetic
marginal
shuffled rank matrix (Algorithm 10))
6: Output: synthetic data X,
The first step (line 2) is generate the matrix M, contain- ing the (uncorrelated) synthetic versions of the marginal distributions of each of the variables in X. The exact proce- dure is described in Algorithms 8 and 9 in the Appendix, but the core process is to separately sample from the marginal distribution of each variable using the interpolated order statistics procedure implemented in Algorithm 3.
Algorithm 3 IOSSampler(x). X²)
While this random interpolation approach generates syn- thetic data whose marginal distributions closely approximate the original data, it does not preserve any of the statistical associations between the variables. To fix this issue, the second step (implemented in lines 3 to 5 of Algorithm 2) is to induce an association structure in the marginal synthetic data which closely approximates the association structure of the real data (without changing the marginal distributions of the synthetic data). The result is a synthetic dataset which approximates well the joint probability distribution of the real data. More precisely, in line 3, Algorithm 2 applies SJPPDS to the real data matrix, X, to obtain a perturbed (partially shuffled) data matrix X which approximates the joint probability distribution of X.
I: Input: subsampled data vectors X1 and Xy of length m
2: 81 + Sort(x1) (sort the values of )
3: S2 + Sort(X2) (scet the values of x2}
4: x +-1 [ [create empty voctor)
5: for
1 to m do
6: a Min(s [1), [1]) (find min between s1 [+] and s2l1)
7:
b 4- Max(s) [i]. [i]) (find the between su and [z(
8:
x|i] < Uniform (a. b) (sample value the b] interval)
9: end for
10: Output: vector of interpolated samples x
The basic idea is the following. For each variable, Algo- rithm 3: (i) takes as input 2 random subsamples (x) and X2) of size m from the original data (line 1); (ii) sort the 2 subsamples, so that the ith element of each subsample correponds to the ith order statistic of the subsample (lines 2 and 3); and (iii) for each index of the sorted subsamples, the algorithm generates synthetic data by randomly sampling a value within the range of these two values (lines 6 to 8).
In line 4. Algorithm 2 computes the matrix of ranks from the shuffled data, R (where each column of R. contains the ranks of each of variable (column) of the shuffled data).
Finally, in line 5 the algorithm performs a rank- matching operation which essentially replaces the shuffled rank val- ues by synthetic marginal values with identical ranks. This last step essentially rearranges the row positions of each variable in the synthetic marginal data in a way that recov- ers the statistical association structure of the shuffled ranks (which, by their turn, approximate the association structure of the real data). This rank mankmatching operation was origi-
Since Algorithm 3 generates only synthetic data-points, in order to generate n samples, Algorithm 9 (in the Ap- pendix) repeatedly calls Algorithm 3 until it generates n (or more) synthetic lata-points (and, if the total number is larger than n, randomly sample n of these points).
4

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
nally proposed by Domingo-Ferrer and Muralidhar (2016) in different context. For completeness we describe it in Algorithm 10 in the Appendix.
Table 2. A toy example of the rank-based numeric encoding of categorical data performed by Algorithm 11 (in the Appendix),
mapR,
A = {1, 3),
B = {4, 5),
C = {6, 8,9)
4.2. The CategoricalSJPPDS Approach
X1 R
A
A
A
B
B
C
C
C
C
2
4
7
The CategoricalSIPPDS approach (Algorithm 4) extends the SJPPDS to categorical data. At a high level, the basic procedure is to: (i) transform the categorical data to ranks; (ii) perform SJPPDS on the ranks; and (iii) transform back the shuffled ranks to categorical data.
Table 3. Rank-based numeric encoding for the alternative ordering,
C A < B, of the levels of the categorical variable Xi.
mapR;
C = {1, 3, 4).
A =
(5, 6,77, B = {8,9) 9}
X, R4
A
A
A
B
B
C
C
C
C
Algorithm 4 CategoricallSIPPSSCX. n².)
7
5
6
9
8
4
3
1
I: Input: categorical data matrix X; number of levels ne
2: (mapR, R. < Categorical CeggoricalToooumeen ToNumeric(X) (call Alg. 11)
3: R + SUPPDS (R, ne) {sall Algoricum 6 in the Appendix)
tied elements C' in X1. Algorithm 11 essentially applies this encoding procedure to all columns of X to produce the numerical rank encoding matrix R.
4: X, f NumericTo Categooriia ,mapa) fcall Alg. 12)
5: Output: synthetic data X,
Once R is created, Algorithm 4 performs SJPPDS on R to generate a shuffled version of the encoded data (with a similar joint probability distribution as R), which is then transformed back (shuffled) categorical data using Algo- rithm 12 (presented in the Appendix).
Step (i) is performed in line 2 of the algorithm, which: (a) creates a mapping (denoted mapR) between the values (lev- els) of each categorical variable in the dataset X and an (arbitrary) numeric rank variable; and (b) encodes the cate- gorical data into the numeric rank data matrix R according to the mapping mapn- (This procedure will be explained in more detail below.) Step (ii) is performed in line of the algorithm, which applies SJPPDS to the encoded nu- merical rank data. Finally, step (iii) is performed in line 4 which transforms back the shuffled numeric rank data to categorical data using again the mapping created in line 2.
Quite importantly, note that this numeric encoding proce- dure is necessarily arbitrary, since the levels of categorical variables have no intrinsic order, and distinct orderings gen- erate distinct numerical rank encodings. (This is illustrated in Table 3, for the distinct ordering C < A B, where Ri in Table 3 is different from Rí in Table 2.)
This arbitrariness, however, does not affect the performance of the CategoricalSJPPDS approach because the same map- ping used to transform X to R is also used to transform R* back to X,, Appendix provides an illustration of this point.
A detailed description of the numeric rank encoding proce- dure in line 2 of Algorithm 4 is presented in Algorithm 11 in the Appendix. But the basic idea is to encode the categorical variables using (arbitrary) numeric rank assignments (with ties broken at random). Table 2 provides an illustrative toy example.
4.3. The MixedSSythhetiSJJPPDS Approach
Let X1 = AA, column of a categorical data matrix X. This categorical variable has three levels A, B, and C with counts n, = 3, ng 2, and ni 4. To generate the numerical rank encoding R2 presented in Table 2, the algorithm transforms the categorical values according to the mapping, mapR, in Table 2. Note that this mapping corresponds to an arbitrary ranking of the categorical levels according to the arbitrary order A < B- < C. That is, starting with class A, the mapping assigns ranks 1, 2, and (in random order) to the three tied elements A in Xi. (Note that by assigning the ranks in random order the mapping is effectively using the "at random" method to break ties among identical values of the categorical variable.) Continuing with class B, the mapping assigns ranks 4 and (in random order) to the two tied elements B in X1. Finally, for class C, the mapping assigns ranks 6, 7, 8, and 9 (in random order) to the four
represent the first
For mixed datasets, Algorithm 5 describes how to prop- erly account for the joint statistical associations between numeric and categorical variables. (Note that separate ap- plications of SyntheticSJPPDS to the numerical variables and of CategoricalSJPPDS to categorical variables preserves the associations among the numeric variables themselves and the associations among the categorical variables them- selves, but destroys any associations between numerical and categorical variables.)
To also preserve the association structure between numeric and categorical variables Algorithm 5 first computes the numerical rank encoding matrix of the categorical data (line 6). before it applies SJPPDS to the concatenated data of numerical variables and numerical rank encodings (lines 7 and 8). By shuffling the concatenated data, the algorithm ensures the preservation of the joint probability distribution
5

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
of all variables (numeric and categorical). After this is done, the algorithm transforms back the shuffled ranks of the numerical variables to synthetic numerical data (lines 9, 10, and 11), and the shuffled rank encodings to shuffled categorical data (line 12).
Table 4. Datasets used in the experiments. (ahbr: abbreviated name; # samples: number of samples; # num: number of numeric variables; # cat: number of categorical variables; task: leaming task (regression classification) Number of variables corresponds to the number of features plus the target.
Algorithm 5 MixedSyntheieSSIPDSSCX in. &er Te. p)
abhr
name
# samples
task
AB
Ahalone
4177
8
regr-
1: Input: data matrix X; indexes of the numeric variables in indexes of the categorical variables ios number of levels ne:; sampling proportion p
AD
Adult
45222
2
13
class.
BM
Bank marketing
10578
7
1
class.
CH
California housing
206400
9
0
regr.
CR
Credit
16714
10
class.
2: X, < -[ 2m] (numerical dataset)
DI
Diabetes 130US
71090
7
class.
Electricity
38478
7
clas.
3: X < [ (categorical dataset)
EM
Eye movements
7608
20
class.
4: nnms + ColumnNames! (x.) (names of numeric variables)
HO
House I6H
13488
16
class.
MT
Magic telescope
13376
10
class.
5: cnms + ComemnNames x (names of categorical variables)
MU
Mushroom
8124
0
21
class.
6: {mapR, R
Categorica/ToNuumrric (X.) (obtain
PO
Pol
10082
26
class.
mupping and numerical rank encuding for the calegorical data)
7: W Concatenate X,., R..) (soncatenate the numeric data and
These selected baselines correspond diverse and repre- sentative sample of tabular data generators in the literature, including strong baselines such as DDPM and ARF. (See ad- ditional comments regarding baseline selection in Appendix G.1.) Details about hyperparameter optimization for the baseline models are described in Appendix G.2.
numerical rank encoding of the categorical data}
8:
W SJPPDS (W, ne) (perform SJPPDS on the concatenated
numeric data]
9:
M. f-
GGenenteSythheiicMaginnnnlSSSSS PX: (create
syathetic marginal distributions for the numeric variables}
10: R DataRankMaatris (W* nnmss) {create matrix
The generator's performances were evaluated with respect to fidelity, utility, and privacy using Synthcity's 's Ben chna rks function. Fidelity was measured using the xgb detection test metric which reports the AUROC for XGBoost classi- fier trained to distinguish real and synthetic data. Utility was evaluated using ML efficiency based on a XGBoost learner trained on the synthetic data and evaluated on the real test data. Privacy was evaluated using the Domias MIA metric (van Breugel et al., 2023). All benchmark experiments were replicated 10 times.
ranks from the shuffled numeric variables)
11: W n f MatchRanks (M, R,;) (rank-match the synthetic
marginal data to the shuffled rank data from the numeric variables)
12: We f
CaaterrrTCCttegoiicacll [W"[, cnms), mOpR.)
(transfrom the shuffled numeric rank encoding data from the categorical vari- ables back to categorical data
13: X f- Concatenate W...
n. W.)
(concalenate numeric
categorical matrices)
14: X, f [ ColumnNames [X] (reander the columns to match
the order in the original data)
15: Output: synthetic data X,
For datasets containing mostly numeric variables, we also evaluated data privacy by comparing the distributions of the distance to closest record (DCR) between synthetic and real samples in terms of Fuclidean distance.
5. Experiments
In our experiments, we compared synthetic data generators across 12 datasets (see Table 4) including 10 mixed datasets (evaluated in Hansen et al., 2023), exclusively categorical dataset (Mushroom), and exclusively numerical dataset (California housing). Further details about these datasets are provided in Appendix G. All datasets were randomly split into training and test sets of approximately same sizes. We performed two sets of experiments.
5.2. Experiment Set
In the second set of experiments, we evaluated privacy risks with respect to DCR and two alternative metrics (imple- mented in R): the sorted version of the Distance Based Record Linkage (SDBRL) metric, which measures robust- ness to re-identification attacks; and the sorted version of the Standard Deviation Interval Distance (SSDID) metric, which measures robustness to attribute disclosure attacks. (See Appendix G.3 for details). Fidelity was again measured using the detection test. We considered the same bascline models as before, in addition to SMOTE (Chawla, 2002).
5.1. Experiment Set 1
In the first set of experiments, we compared TabSDS against 5 general purpose generators available in Synthcity, namely: tabular denoising diffusion probabilistic models (DDPM); adversarial random forests (ARF); tabular variational au- toencoders (TVAE); conditional tabular generative adversar- ial networks (CTGAN); and bayesian networks (BayesNet).
5.3. TabSDS Tuning Parameter Selection
TabSDS relies on only two tuning parameters. The first is the p parameter in Algorithm 8 which controls the quality
6

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
of the synthetic marginal distributions by controlling the subsample size, m, used in Algorithm 3. Overall, we found that lower values of p can lead to accentuated decreases in data fidelity without comparable increases in data privacy. (See Appendix G.9 for these evaluations.) For this reason we adopt p = 0.5 (the maximal value) in our evaluations. The second, and more critical parameter, is the number of levels/categories, ne, used by the restricted permutations. This parameter controls the amount of shuffling applied to the data and allows for more precise control of the trade-off between data fidelity/utility and data privacy.
independent samples from the same distribution as the train- ing data (as our training and test sets have identical sizes). The red horizontal line corresponds to the median of the test set DCR distribution. DCR distributions whose medians are located below the red line show reduced privacy when compared to an ideal generator, while distributions whose medians are above the red line show increased privacy. For both datasets, we observe that low ne values tend to gen- erate synthetic data which is more private than truly i.i.d. dataset, but that larger The values lead to synthetic datasets that are closer (in terms of DCR) to the training data. In- terestingly, some datasets show a much faster decrease in DCR than others (compare panels b and a).
The ne parameter can take any value between 1 and n (the number of samples in the real dataset). Setting n. = 1 leads to maximum shuffling, as allows for unrestricted permu- tations of the data and completely removes the association between the variables. Larger values of ne constrain the amount of shuffling, leading to higher fidelity and decreased privacy. In the limit case when n. = n, the data is not shuf- fled. (See Figure 11 in the Appendix for an illustration of
(8] DCR distributions (CH)
012
DCR distributions (EL)
0.05-
0.00-
0.04-
0.00
3 2'
000
n00
1000
20
30
an
the effect of ne on the synthetic data quality.) In our experi- ments, we evaluate TabSDS over grid of 24 values, n. = (5, 10, 15, ... 50, 60, 70, 100, 200, 300, ...0, 1000].
Figure 4. DCR distributions for the CH (a) and EL (b) datasets.
These results clearly illustrate that the quality of the syn- thetic data improves with increasing values of ne (as illus- trated by the increasing ML efficiencies in Figures 2b and 3b, and decreasing ability to discriminate between real and synthetic data in Figures 2a and 3a). However, increases in ne also lead to lower privacy protection, illustrated by the higher accuracies of the membership inference attacks in Figures 2c and 3c, and by DCR distributions concentrating closer to O in Figure 4.
To illustrate the tradeoff between fidelity, utility, and privacy, Figures 2 and 3 report the detection test metric (panel a), ML efficiency (panel b), and domias MIA (panels c) for synthetic versions of the CH and EL datasets generated by the TabSDS approach over the grid of ne values above.
Detection test
0.80
ML efficiency
Domias MIA
0,90
000000009
(a)
0.50
metic
0.5
metric
0,55
metric
This ability to exert a precise control over the trade-off between data utility/fidelitty and data privacy is a very attrac- tive feature of TabSDS, In practice, an analyst can inspect this trade-off over grid of n. values across several utility, fidelity, and privacy metries to select adequate value for the intended application. For our comparisons, we selected The as follows. For datasets containing mostly numerical variables we used the DCR distributions and selected the largest n. value in our grid which generates a DCR distribu- tion with a median value close to the median of the test set DCR distribution. (In the examples in Figure 4, we select ne equal to 200 and 20.) For datasets containing mostly cat- egorical variables we selected the largest which balanced well the tradeoff between the detection test, ML efficiency, and Domias MIA metrics. In Appendix G.5, we describe the tuning parameter selection for all 12 datasets evaluated in this work.
0.60
0
0.50
(b)
0.4
(c)
400
800
800
400
800
ne
nn
ng
Figure Benchmark metrics over the n. grid for the CH dataset.
Detection test
ML efficiency
Domias MIA 0000000
0,90
00000603
0.95
(a)
metric
metric
metric
0.52
0.80
0.85
(b)
0.50
(c)
400
800
400
800
400
800
fic
Figure 3. Benchmark metrics over the ne grid for the EL dataset.
To further illustrate the effect of ne on privacy, Figure 4 shows the distributions of the distance the closest record (DCR) between the synthetic and real training samples (white boxplots) for datasets CH and EL.. For comparison, it also shows the DCR distribution between the training and test set data (grey boxplots). Note that the grey boxplots provide an estimate of the typical DCR values we would expect to see from an ideal generator capable of drawing
5.4. Results
1. EXPERIMENT SET I
Tables 5, 6, and 7 report the benchmark results for the fi- delity, utility, and privacy metrics, respectively. In each
7

---

TabSDS: a Lightweight, Fully Non- Mon-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
table, the top 2 generators were highlighted in bold. Over- all, TabSDS showed very competitive performance against strong baselines such as DDPM and ARF. In terms of fi- delity and utility, in most datasets, it either ranked first or second, intercalating these top positions with DDPM and ARF, In terms of privacy, none of the generators stood-up as systematically outperforming the others.
Table 7. Privacy comparisons as measured by domias MIA. The
table reports average AUROC and standard deviations (in paren- thesis).
Lower values imply better performance.
dataset
TakSDS
DDPM
ARF
TVAE
CTGAN
BayesNer
AB
0.531
0.541
0.523
0.555
0.555
0,503
(0.017)
(0.019)
(0.023)
(0.044)
(0.046)
(0.038)
AD
0.766
0.703
0.724
0.716
0.698
0.635
(0.009)
(0.01)
(0.013)
(0.021)
(0.024)
(0.015)
BM
0.377
0.332
0.361
0.376
0.360
0.400
(0.003)
(0.007)
(0.006)
(0.009)
(0.023)
(0.010)
Table 5. Fidelity comparisons as measured by the detection test metric. The table reports average AUROC and standard deviations
CH
0.492
0.512
0.575
0.472
0.442
0.640
(0.004)
(0.011)
(0.015)
(0.05)
(0.022)
(0.021)
CR
0.345
0.477
0.334
0.399
0.362
0.380
(in parenthesis). Lower values imply better performance.
(0.006)
(0.083)
(0.01)
(0.035)
(0.030)
(0.011)
dataset
TabsDS
DDPM
ARF
IVAE
CTGAN
BayesNet
D1
0.51
0.491
0.473
0.454
0.491
0.468
AB
0.837
0.878
0.981
0,995
0,994
1,000
(0.004)
(0.005)
(0.013)
(0.01)
(0.028)
(0.009)
(0.021)
(0.007)
(0.004)
(0.002)
(0.002)
(0.000)
EL
0.506
0.521
0.536
0.519
0.527
0.431
AD
0.69
0.782
0.877
0.997
0.998
1,000
(0.003)
(0.005)
(0.01)
(0.013)
(0.031)
(0.016)
(0.004)
(0.007)
(0.006)
(0.001)
(0.001)
(0.000)
FM
BM
0.693
0.697
0,996
0.999
0.999
0.998
HO
(0.043)
(0.005)
(0.001)
(0.000)
(0.000)
(0.000)
MT
0.375
0.342
0.344
0.387
0.406
0.426
CH
0.721
0.647
0.965
0.976
0.971
0.993
(0.005)
(0.007)
(0.013)
(0.016)
(0.016)
(0.011)
(0.028)
(0.004)
(0.002)
(0.001)
(0.002)
(0.001)
MU
0.646
0.612
0.612
0.603
0.572
0.636
0,852
0.769
0.997
10000
1.000
0.999
(0.018)
(0.129)
(0.029)
(0.046)
(0.057)
(0.027)
(0.006)
(0.021)
(0.000)
(0.000)
(0.000)
(0.000)
PO
0.772
0.789
0.744
0.749
0.762
0.762
DI
0.627
0.589
0.990
1,000
1.000
0,999
(0.008)
(0.009)
(0.009)
(0.014)
(0:007)
(0.009)
(0.023)
(0.004))
(0.000)
(0.000)
(0.000)
(0.000)
E.
0.976
0.802
0.980
0.998
0,999
0,999
(0.001)
(0.003)
(0:001)
(0.000)
(0.000)
(0.000)
Table 8. Average runtime in seconds.
EM
0.961
1.000
1.000
1.000
1,000
1,000
data
samples
TabSDS
BayesNet
ARF
DDPM
TYAE
CTGAN
(0.0016
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
AB
2088
1.33
2.86
24.52
282.69
444.13
172.78
HO
0.752
0.748
0,942
0,987
0.989
0.998
22611
5.43
9.50
304.17
699.89
1655.63
1046.77
(0.006)
(0.009)
(0.002)
(0.001)
(0.002)
(0.000)
RM
5289
2.99
3.87
17.38
93.21
314.36
277.35
MT
0,720
0.631
0.817
0,948
0,958
0.996
10320
7.76
21.99
82.89
980.76
261.
997.33
(0.004)
(0.005)
(0.007)
(0.004)
(0.008)
(0.000)
CR
8357
9.23
6.43
35.15
195.42
543.87
504.83
MU
0.664
0.954
0.700
0,887
0.872
0.908
D1
35545
22.98
14.06
116.92
616.87
1887.39
1148.02
(0.005)
(0.039)
(0.008)
(0.021)
(0.060)
(0.005)
EL
19237
11.17
11.77
86.42
337.81
1006.72
782.99
0.955
0.980
0.997
1.000
1.000
0,999
EM
3804
6.40
13.47
84,35
97.10
291.14
321.38
(0.006)
(0.003)
(0.000)
(0.000)
(0.000)
(0.000)
HO
6744
14,95
55.77
131.26
121.44
407.68
357.32
MT
6688
5.43
32.05
42.51
123.36
382,79
389.47
Table 6. Utility comparisons measured by ML efficiency. The table reports average AUROC for classification tasks and aver- age RD for regression tasks (with standard deviations reported in
MU
4062
1.22
2.27
51.68
2203.03
327.70
726.17
PO 5041
10.31
13,90
202.36
94.95
367.63
428.78
also considerably faster than ARF. (In most datasets it even outperformed the BayesNet generator.)
parenthesis). Higher values imply better performance.
datasel
TabSDS
DDPM
ARF
TVAE
CTGAN
BayesNet
0.511
0.524
0.466
0.347
0.363
-0.003
(0.028)
(0.019)
(0.028)
(0.050)
(0.049)
(0.064)
AD
0.885
0.877
0.882
0.845
0.851
0,863
5.4.2. EXPERIMENT SET 2
(0.003)
(0.003)
(0.003)
(0.006)
(0,008)
(0.004)
BM
0.849
0,839
0.836
0.793
0.790
0.558
Figure 5 reports privacy vs fidelity tradeoff curves compar- ing the DCR, SDBRL, and SSDID privacy metrics against the detection test AUC fidelity metric. (Due to space limita- tions the figure only report results for the Abalone (AB) and Bank marketing (BM) datasets. The complete results for all datasets are presented in Figures 24 and 25 in Appendix G.6.) In addition to the baselines in the previous experiment these results also include comparisons against the SMOTE baseline (Chawla et al., 2002) based on k = 5 and k = 20 neighboors. Panels a and b shows the tradeoff between DCR vs detection AUC, The red vertical line represents the DCR score comparing the training and test sets and provides an estimate of the DCR value we would expect to see for an ideal generator able to draw i.i.d. data from the same distri- bution as the training data. The black curve represents the TabSDS results across the entire n. parameter grid, while the red dot corresponds to the TabSDS performance based on the ne value selected according to the DCR criterium (i.e., the DCR value closest to the test set DCR). Panels
(0.006)
(0.003)
(0.006)
(0.016)
(0.018)
(0.038)
CII
0.777
0.769
0.658
0,583
0.595
..1156
(0.005)
(0.004)
(0.012)
(0.014)
(0.012)
(0.021)
CR
0.817
0.831
0.838
0,787
0.783
0.779
(0.005)
(0.006)
(0.005)
(0.018)
(0.018)
(0.012)
DI
0.611
0.621
0.625
0,561
0.579
0.616
(0.005)
(0.003)
(0.004)
(0.023)
(0.031)
(0.005)
EL
0.836
0.589
0,889
0.821
0.806
0.657
(0.003)
(0.003)
(0.005)
(0.010)
(0.023)
(0.024)
EM
0.600
0.485
0.533
0.540
0.523
0,530
(0.019)
(0.034)
(0.032)
(0.027)
(0.027)
(0.019)
HO
0.949
0.947
0.914
0.922
0.892
0.488
(0.001)
(0.002)
(0.006)
(0.084)
(0.011)
(0.043)
MT
0.912
0.918
0.885
0.862
0.843
0.497
(0.004)
(0.004)
(0.009)
(0.010)
(0.013)
(0.039)
MU
1,000
0.621
1.000
0.998
0.989
0.993
(0.000)
(0.138)
(0.000)
(0.002)
(0.004)
(0.001)
PO
0.99
0.911
0.968
0.931
0.848
0.905
(0.002)
(0.007)
(0.003)
(0.018)
(0.056)
(0.007)
Table 8 reports the combined runtime for model training and data generation (in seconds) of each generator across all datasets. (See Appendix G.7 for runtime experiment details.) In all datasets, the runtime for TabSDS was orders of magnitude faster than the deep generative models, and
8

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
and d show the tradeoff plots comparing SDBRL vs de- tection AUC, while panels and f report the tradeoff plots
generate more realistic data than alternative generators.)
between SSDID vs detection AUC.
6. Limitations
Detection test AUC (smmllee beiter)
1.00
(a) Abalone (AB)
Detection test AUC (amalles beterr
(b) Bank marketing (BM)
An important limitation of TabSDS is that, being a model free approach, it cannot be adapted to the generation of fair synthetic data. (State-of-the-art approaches such as DECAF (van Breugel et al., 2021) require modeling the syn- thetic data generation process according to a causal model representation of the data generation process). The main application of TabSDS is to facilitate data sharing, where synthetic versions of real data can be more readily shared. (This application is what motivated its development.)
0.95
TabSOs
0.90
sel
DDPM
0.85
ARF
0.00
TIVEE
CTGAN
0.75
NayesNet
40
SMOTE K20
0.70
SMOTE_K K5
300
0.05
%
1000
0.00
0.10
0.20
20
25
DCR
DCR
Detectio less AUC (streler, better)
1.00
(c)
Abalone (AB)
Detection less AuS (srraller, beter)
(d)
Bank marketing (B (BM)
0:95
A minor caveat of the proposed IOSSampler method (AI- gorithm 3) for generating marginal distributions is that for discontinuous multimodal distributions, where training val- ues cluster near separate modes with no training examples in between, the method may generate a small fraction of in- termediate values outside the training data range (see Figure 69 for an illustration). In these situations, a pooc-proes step could be easily added to remove values outside the range of the training data.
0,30
0.05
n_c
0.00
0.75
0.70
00
0.00
8
1000
0.00
0.10
0.20
0.30
0.00
0.01
0.02
0.03
D Disclosure risk in SDBRL Ismaller, betrar)
Disclosune risk in SDBRL (smailer, betteri
Detection best AUC (smeller betor)
1,00
(e)
Abalone (AB)
Detection AUC tsmeller, beter)
(f)
Bank marketing (BM)
0,95
0.00
7. Conclusions and Final Remarks
0.09
P_c
00 00
0,90
We introduce a simple, lightweight, fully non parametric, and model free approach for the generation of synthetic tab- ular data. The work extends data perturbation methodology from the statistical disclosure control field, and provides very competitive performance against strong baselines in the ML field, at fraction of the runtime.
0.75
0.70
00
0
0.05
90
1000
0.00 0.05
0.15
0.000
0.005 0.010
0.015
Disclssrre rik in SSDID (smaller, better)
Disclosure risk in SSDID (smaller, better)
Figure 5. Privacy/utlility tradeoff comparisons for the Abalone
(AB) and Bank marketing (BM) datasets. See legend on panel a.
While the interpolated order statistics approach proposed in this paper performed well in our experiments, an interesting future research avenue is to evaluate alternative approaches for the generation of the synthetic marginal distributions. (Note that any method for generating uncorrelated synthetic marginals can be directly plugged into line 2 of Algorithm 2. Since the generation of marginal synthetic data should, in principle, be easier than the generation of joint distributions, this could lead to the development of hybrid approaches, where the uncorrelated marginals are generated with para- metric models, while the association structure is recovered in a non parameeetttic way.) Another interesting future re- search direction is the incorporation of differential privacy into the TabSDS approach.
Overall, in these two datasets, DDPM (purple filled square), SMOTE (purple crossed diamond and purple crossed circle), and TabSDS (red filled circle) tended to outperform the other methods in terms of fidelity (note the lower AUC scores for the detection test in the y-axis). In terms of privacy. SMOTE tended to be worse than the other methods with respect to DCR (note the lower DCR values in panels a and b). In terms of SDBRL and SSDID, all methods tended to generate low risk scores with SMOTE tending to perform slightly worse than the other methods.
Appendix G.6 reports a more detailed evaluation across 10 datasets. Overall, similar results hold for the other datasets. In addition to the baselines investigated here, the results in the Appendix include additional comparisons against two differential privacy based generators, well as, against simple additive noise perturbation method.
Finally, note that while the TabSDS approach treats any numerical variables as real valued, for any integer valued variables in a dataset, we recommend the use of a post- processing step for rounding the data of these variables to the nearest integer value.
Finally, Appendix G.8 presents qualitative comparisons of how well these different generators mimic the marginal distributions and statistical associations in the real data. (These last evaluations suggest that TabSDS can, overall,
R and Python implementations of TabSDS are available https://gi hhu. com/ hcmmaecchbbbb///// haaibbubbT/bbb..... TabSDS.

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Impact Statement
[1]] Domingo-Ferrer, J., and Muralidhar, K. (2016). New directions in anonymization: permutation paradigm, verifiability by subjects and intruders, transparency to users. Information Sciences, 337-338: 11-24.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
[12] Domingo-Ferrer, J., Muralidhar, K., and Bras-Amoros M. (2020). General confidentiality and utility metries for privacy-preserving data publishing based on the permutation model. IEEE Transactions on Depend- able and Secure Computing, 1865):200-22517. DOI: 1..11//TDCC.2002226800000
References
[1] Akiba, T., Sano, S., Yanase, T., Ohta, T., and Koyama, M. (2019). Optuna: A next-generation hyperparameter optimization framework. In Proceedings of the 25th ACM SIGKDD International Conference on Knowl- edge Discovery & Data Mining (pp. 2623-2631).
[13] Domingo-Ferrer J., Muralidhar, K., and Martinez, S. (2025). Synthetic data generation via the permutation paradigm with optional k-anonymity. IEEE Transac- tions on Dependable and Secure Computing PP(99))1-
[2] Bond-Taylor, S., Leach, A., Long, Y., and Willcocks, C. G. (2021). Deep generative modelling: a compara- tive review of vaes, gans, normalizing flows, energy- based and autoregressive models. IEEE Transactions on Pattern Analysis and Machine Intelligence.
12, 2025.
[14] Domingo-Fert Ferrer, J., Sanches, D., and Ruffian-Torie G. (2013). Anonymization of nominal data based on semantic marginality. Information Sciences, 242, 35- 48.
[3] Borisov, V., Sessler, K., Leemann, T., Pawelczyk, M., and Kasneci, G. (2022). Language models are realistic tabular data generators, in: The Eleventh In- ternational Conference on Learning Representations (ICLR), 2023.
[15] Domingo- J., and Torra, V. (2001). A quanti- tative comparison of disclosure control methods for microdata. In Confidentiality. disclosure, and data ac- cess: theory and practical applications for statistical agencies, edited by P. Doyle, J. Lane, Theeuwes, and I., Zayatz. 111 133. Elsevier.
[4] Brand, R. (2004). Microdata protection through noise addition. In Privacy in Statistical Databases. Lecture Notes in Computer Science. Springer, pages 347359.
[5] Burridge, (2003). Information preserving statistical obfuscation. Statistics and Computing, 13: 321-327. http:pp//...bboooooo/o..//1///10
[16] Drechsler, J. 1). Synthetic Data Sets for Statistical Disclosure Control. Springer. New York.
[17] Drechsler, J., and Haensch, A. (2024). 30 years of synthetic data. Statistical Science, 39(2): 221-242.
[6] Cano, I., and Torra, V. (2009). Generation of syn- thetic data by means of fuzzy c-regression. 1145-1150.
10.1 1A,1099FU22Y.2209557770000
[18] Drechsler, J., and Reiter, J.P. (2011). An empirical evaluation of easily implemented, nonparametric meth- ods for generating synthetic datasets. Computational Statistics and Data Analysis, 55, 3232-3243.
[7] Chaibub Neto, E. (2024). Statistical disclosure control for numeric microdata via sequential joint probabil- ity preserving data shuffling. Transactions on Data Privacy, 17(3):14--179, 2024.
2024.
[19] Du Y., and Li, N. (2025). Systematic assessment of tabular data synthesis algorithms. Proceedings of In- ternational Conference on Management of Data (SIG- MOD'25).
[8] Chawla, N. V., Bowyer, K. W. Hall, L. O., and Kegelmeyer, W. P. (2002). Smote: synthetic minority over-sampling technique. Journal of Artificial Intelli- gence Research, 16, 321-357.
[20] Fang. X., Xu, W., Anting Tan, F., Zhang, J., Hu, Z., Qi. Y., et al. (2024). Large language models on tabular data a survey, arXiv e-prints, arXiv-2402.
[9] Cresswell, J. C., and Kim, T. (2024). Scaling up diffusion and flow-based XGBoost models. arXiv 1608.16046
[21] Hansen, L., Seedat, N., van der Schaar, M., and Petro- vic, A. (2023). Reimagining synthetic tabular data generation through data-centric AI: A comprehensive benchmark. Advances in Neural Information Process- ing Systems, 36, 33781-33823.
[10] Domingo-Ferrer, J., and Mateo-Sanz, J. M. (2002). Practical data-oriented microaggregation for statistical disclosure control. IEEE Trans. on Knowledge and Data Engineering, 1411:189-201.
10

---

TabSDS: Lightweight, Fully Non- Non-Paramettrc, and Model Free Approach for Generating Synthetic Tabular Data
[22]
Jolicoeur-Martneeau, A., Fatras, K., and Kachman, T. (2024). Generating and imputing tabular data via diffu- sion and flow-based gradient-boosted trees. AISTATS
[34] Reiter, J. P. (2005). Using CART to generate partially synthetic, public use microdata. Jouraa of Official Statisties, 21(3):41-462.
2024
[35] Reiter. J. P. (2023). Synthetic data: look back and a look forward. Transactions on Data Privacy, 16, 1524, 2023.
[23] Jordon, J., Yoon, J.. and Mihaela van der Schaar, M. (2019). PATE-GAN; generating synthetic data with differential privacy guarantees. ICRL 2019.
[36] Shi, J., Xu, M., Hua, H., Zhang, H., Ermon, S., and Leskovee, J. (2025). TabDiff: a mixed-type diffusion model for tabular data generation. ICLR 2025.
[24] Kindji, G. C., Rojas- Bataaoaa L. M.. Fromont, E., and Urvoy, T. (2024). Under the hood of tabular data generation models: benchmarks with extensive tuning. 1XXv:22466.1245
[37] Van Breugel, B., Kyono, T., Berrevoets, J., and Van der Schaar, M. (2021). Decaf: Generating fair syn- thetic data using causally-aware generative networks. Advances in Neural Information Processing Systems, 34, 22221-22221
[25] Kotelnikov, A., Baranchuk, D., Rubachev, I., and Babenko, A. (2023). Tabddpm: Modelling tabular data with diffusion models. In International Conference on Machine Learning (pp. 17564-17579). PMLR.
[38] Van Breugel, B., Sun, H., Qian, Z., and van der Schaar, M. (2023). Membership inference attacks against syn- thetic data through overfitting detection. AISTATS 2023.
[26] Langsrud, O. (2019). Information preserving
regression-based tools for statistical disclosure control. Statistics and Computing, 29, 965976.
[39]
Watson, D. S., Blesch, K., Kapar, J., and Wright, M. N. (2023). Adversarial random forests for density esti- mation and generative modeling. International Con- ference on Artificial Intelligence and Statistics (pp. 5357-5375). PMLR.
[27] Lu, Y., Wang, H., and Wei, W. (2023). Machine learn- ing for synthetic data generation: a review. arXiv preprint arXiv:2302.00m:
2023.
(28) Mateo-Sanz, J.M., Sebe, F., and Domingo-Ferrer, J. (2004). Outlier protection in continuous microdata masking. International Workshop on Privacy in Sta- tistical Databases. PSD 2004: Privacy in Statistical Databases pp 201-215.
[40] Xu, L., Skoularidou, M., Cuesta-Infante, A., and Veeramachaneni, K. (2019). Modeling tabular data using conditional GAN. Advances in Neural Informa- tion Processing Systems, 32, 2019.
[41] Yoon, J., Drumright, L. N., and van der Schaar, M. (2020). Anonymization through data synthesis using generative adversarial networks (ADS-GAN), IEEE Biomed Health Inform., 24, 2378-2388.
[29] Moore, Jr R. (1996). Controlled data-swapping tech-
niques for masking public use microdata, U.S. Bureau of the Census Statistical Research Division Report Series, RR 96-04.
[42] Young, J., Graham, P., and Penny, R. (2009). Using bayesian networks to create synthetic data. Journal of Official Statistics, 25(4)5549.
[30] Muralidhar, K., and Sarathy, R. (2006). Data shuffling new masking approach for numerical data, Manage- ment Science, 52, 658-670.
[43] Zhang, H., Zhang, J., Srinivasan, B., Shen, Z., Qin, X., Faloutsos, C., Rangwala, H., and Karypis, G. (2023). Mixed-type tabular data synthesis with score-based diffusion in latent space. in: The Twelfth International Conference on Learning Representations, 2024.
[31] Nowok, B., Raab, G. M., and Dibben, C. (2016). synthpop: bespoke creation of synthetic data in R. Journal of Statistical Software, 74(11), 1-26. https//db...rg/1...66///ss..
[32] Pagliuca, D., and Seri, G. (1999). Some results of in- dividual ranking method on the system of enterprise accounts annual survey, Esprit SDC Project, Deliver- able MI-3/D2.
[33] Qian, Z., Davis, R., and van der Schaar, M. (2024). Synthcity: a benchmark framework for diverse use cases of tabular synthetic data. Advances in Neural Information Processing Systems, 36.

---

TabSDS: Lightweight, Fully Non-Parametre and Model Free Approach for Generating Synthetic Tabular Data
A. SJPPDS Algorithms
For completeness, we present below the SJPPDS algorithm. (See Chaibub Neto (2024) for a detailed description of the algorithm.) While the original paper proposes two versions of joint probability preserving data shuffling, namely, the "full" and "simplified" data shuffles, in this paper we only consider the simplified version, as is considerably faster than the full one without incurring any loss in performance. (Chaibub Neto (2024) recommends the use of the simplified version in practical applications.)
Algorithm 6 Sequential joint probability preserving data shufiling (SJPPDS)
1: Input: microdata, X; number of classes/levels, ne
2: Find the number of attributes, p. of X, i.e., p < NumberOffoluunns/ X)
3: Create the categorical version of X, denoted C, by discretizing each column of X into ne categories: C CategorizeDatai (X.
4: Generate the masked data, X", by using the JPPDS algorithm: X f- +-uurrrooodiiyyyyeerrrrnouuuuuuu
5: for i = 1 to p do
6: Change the order of the columns of X so that the first column is placed last, i.e., X <- X x',co(2pp
7: Update the categorical version of the masked microdata, i.c., C' + CategorizeData (X* ,7c)
8: Update the masked microdata, i.e., X* +- JonnPPoohhiiyyysssrrrinaaaauiii X* C**)
9: end for
10: Restore column order to the order in the original dataset, i.e., X <- X'( 1)]
11: Output: return the masked dataset X
Algorithm 7 Joint probability preserving data shuffling simplified version (JPPDS-s)
I: Input: microdata, X; categorical version of the microdata, C
2: Find the number of attributes, p, of X, i.e., p NumberOfColumms((X (X)
3: Find the number of records, n, of X, i.e., n < NumberOrRows(X* (X)
4: Initialize the matrix with shuffled data with the original microdata, i.c., X, + X
5: Get the last column of C, i.e., Cp + Cl.p]
6: Get the unique values of Cp. i... Cpu f- Unique(Cp)
7: Get the length of the Cpu. vector, i.e., The +- Length(Cpm)
8: for j to nl do
9: Find the indexes of Cp that have the value in Cpali]. i.e., idæ <- Cpull)))
==
10: Obtain randomly shuffled version of the indexes in idæ, i.e., idv, <- Shuffle(idx)
11: For the first p- 1 columns, replace the data in the rows of X, indexed by idæ by the data in rows idz, of X, i.e.
Lide, 1: (p- - 1)] + X (idæ., 1 (p- 1)]
12: end for
13: Randomly shuffle the rows of X s, i.e., X, f- X, (Shufflee1 : n).]
14: Output: return the shuffled dataset Xx
B. Additional Algorithms for Generating Synthetic Marginals via Interpolated Order Statistics
Here, we describe in detail the generation of the synthetic marginal distributions. Algorithm 8 is basically wrapper function for separately applying Algorithm 9 to each one of the variables (columns) of the data matrix X.
Algorithm 9 and Algorithm 3 (in the main text) describe the interpolation approach (based on order statistics) used to generate synthetic data from the marginal distributions of each variable. For each variable, the basic idea is to: (i) take random subsamples of size m of the variable data (as described in lines 8 to 10 of Algorithm 9); (ii) sort the 2 subsamples as described in lines 2 and 3 of Algorithm 3 (so that the ith element of each subsample correponds to the ith order statistic of the subsample); and (iii) for each index of the sorted subsamples, the algorithm generates synthetic data by randomly sampling a value within the range of these two values (as described in lines 5 to 9 of Algorithm 3).
Since Algorithm 3 generates only m synthetic data-points, in order to generate n samples, Algorithm 9 repeatedly calls Algorithm 3 until it generates n (or more) synthetic data data-points. (The number of calls is given by [n/m] as described in line of Algorithm 9). If the total number of synthetic samples generated over the [n/m]] calls is larger than n, the algorithm
12

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
randomly sample of these points (as described in line 14).
Algorithm 8 CenermeeSyyhheiiiMMiiindSSSS,,,
1: Input: data matrix X; sampling proportion p
2: n NumberOfRows X) { (find number of rows)
3: k <- NumberOfCols(XX (find number columns}
4: M, f- [.] (ereate empty matrix}
5: for = to k do
6: [] < InceplaaeeOrdeeSStaaaamigngg.
(generate interpolated synthetic marginal data for the jth variable (Algorithm 9)}
7: end for
8: Output: matrix of synthetic marginals M,
Algorithm 9 IncepplatccOrddeSttttSSappppiai p)
1: Input: data vector x; sampling proportion p
2: n + Length(x) [get length x}
3: seq, f Sequence(L, n2) (get a sequence of integers from x)
4: m + Floor(n p) {round down n + p to the nearest integor)
5: ndraws +- Ceiling (n/m) fround up a/ma nearest integer to get the number draws)
6: Y + [,] (create empty m
7: for i = 1 to ndraws do
8: idx <
Withouurppppaccceenttseeet m) (sample vn indexes out of the seg, sequence)
9: idx, f- SetDifference (seDifferennceeeg...... idæ1) fcompute the set difference to obtain the remaining indexes}
10: id.r2 SampleWithoulkeppceeenetff
m) [sample en out of the remaining indexes) Y IOSSampler(x)) [idzi]] x2 [idxz]] [get interpolated sample}
12: end for
13: y +- Vector Y)
(vectorize the Y matrix)
14: y + SampleWithoutRepllceeeen
n) (luke random sample of elements from the y vector)
15: Output: vector of interpolated samples
By randomly interpolating between the values of each order statistic this approach generates synthetic data which approxi- mates the marginal distribution of the original variable data. Intuitively, the quality of the approximation depends on the size of the subsamples, m, with higher values leading to better approximations. As described in line 4 of Algorithm 9, m is computed as m [mp], where n is the number of data points in the dataset and 1/ S p S 0.5.
To illustrate how the subsample size affects the quality of the synthetic data, in Figures 6 and 7 we apply Algorithm 9 (and Algorithm 3) to the same data using p 0.3 and p 0.25.
In these examples we use random sample of size n = 100 from the latitude variable in the California housing (CH) data, as our real data. The blue histograms in Figures 6c and 7e show the real data distribution.
By adopting = 0.5, we have that m = 50, and Algorithm 9 needs to call Algorithm 3 two times in order to generate 100 synthetic datapoints. Figures 6a and show the synthetic data (red points) generated by these two calls. In these panels, X() represent the sorted real data, X()) the sorted synthetic data, and Y()) and Z(a) represent the sorted subsamples of size 50 randomly drawn from X. The grey dotted lines connect the ith order statistics in subsamples Y and Z (which corresponds to the x and X2 vectors in the notation of Algorithm 3). The red histogram in Figure 6c shows the distribution of the synthetic data (computed by pooling together the red dots in panels and b). Finally, Figure 6d shows the quantile-quantile plot comparing the real and synthetic data distributions.
By adopting p = 0.25, we have that m = 25, and Algorithm 3 needs to be called four times to generate 100 synthetic datapoints. Figures 7a to d show the synthetic data generated by these four calls. Figure shows the histograms of the synthetic data and real data, and Figure 7f shows the respective quantile-quantile plot.
Comparisons of the synthetic data histograms in Figures 6c and 7e, well the quantile-quantile plots in Figures 6d and 7f, clearly show that lower values of (or, smaller subsample sizes) lead, as expected, to noisier synthetic data versions of the real data.
13

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
(a)
R1
34
35
40
(b)
guplet
(c)
3
27
2
33
Figure Illustrative application Algorithm with p = 0.5.
(a)
211
(b)
(C)
941
(d)
R41
201
38
40
syth
(e)
355
Figure Illustraiive application of Algorithm 9 with p = 0.25.
14

---

TabSDS: Lightweight, Fully Non-Parametric and Model Free Approach for Generating Synthetic Tabular Data
C. Proof of Theorem 1
Consider a numeric random variable distributed as X ~ Fx. Let Y and represent two subsamples of size m from X. Let,
(1) = -
m
F ()))=
m m Σ 122,51
(1)
m
represent, respectively, the empirical cumulative distribution functions of the Y and Z subsamples, where 1 represents the indicator function. Let,
(1) < ((2) < Y(3)
((m-1) < ((m)
(2)
20) Z22) (
((m-1)
((m)
represent the sorted subsamples, where (()) and (()) represent the ith elements of the sorted subsamples (i.e., the ith order statistics of the subsamples).
Since the interpolated order statistics samples generated by Algorithm 3 are draw from,
(0) Uniform [min(((r Z(0 max(Y Zm))
(3)
we have that, by construction,
(i) 2n0 & (()) s max Z
(4)
Taken together the constraints in equations (2) and (4) imply that for all the empirical cumulative distribution function of the interpolated samples, F* (t), satisfy the relation,
min (in( (2) & (t) S max FT (t)
(5)
See Figure 8 for an illustrative example.
It follows directly from Sdivenko-Cantell theorem that both FY and F% converge almost surely to Fx, converges to infinity. Now, reexpressing.
F. (2)
1P P()(
min (1), (Z)
(6)
max FY (f), (t) FX (1) + (L) + | (1) FZ(())
2
and taking the limit over m, it follows that both min (t), (t) and max FX (t), (t)) converge to Fx. Hence, from (5) it follows that f.t is bounded from above and from below by Fx and, therefore, also converges almost surely to Fx.
15

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
x()
((1)
Y
Y(s)
(6)
Y0
X
X00
Z00
Zg
Z(4)
t-5
t-8
t-11
t-14
t-17
t-20
t-23
t-26
t-29
t-32
t-35
((())= =0
F,0))= =0
=0)
F(t0)
=0.4)=0.4
(0.6)=0.6
=0.6)0066
=0.5
F(()==0.
(0.55
(+)))=
Ar(t)
falt)==
=02
=..
fr(t)
=0.4
=0.6
((())
=0.6
=..))
(r())=1
Fz(1)= =0
=2(0)=0
=o
fz(t)=0 =0
=o
=0.
=..6)=066
f.00)
=0.6
f2(t)=o =0.8
f1(t)=1
fz(t)=1
15
25
Figure Consider. without loss of generality, sorted variable (() (9, 16, 19, 20, 21, 23, 28, 30, 33, 34) (shown by the black dots the top row of figure). Let Y(a) and ((s) represent two sorted random subsamples size from X, and X(a) synthetic data generated by randomly drawing values from Uniform(min) Y(s, Z , max (())) (8), Z(a)), H) for i = I,..., 5. For any value of t, the values of the empirical cumulative distribution functions of Y, X, and Z correspond, graphically. to the proportion of dots at or to the left of the vertical line at For instance, for t 20 (the purple vertical line), there are points to the left of the line for variable Y, points to the left for variable X, and I point at the line for variable Z, implying that (20) 0.6, (20) 0.4. and F2()0) 0.2. Inspection the figure shows that the relation min(Fy (t), (t) I (t) I max (Fx (t)())))))))))))))))))) (t) holds for any value of in the real line.
D. Rank-Matching Algorithm
Algorithm 10 MatchRanks(MML, R)
Input: matrix of synthetic marginal data, M,; matrix of ranks from the original data, R
2: X, []] (create empty matrix)
3: NumberO(Rows(RR {find number of rows)
4: k <- NumberOfCols(BB) (find number columns)
5: for j to i do
6: <- Rank(M, (M,) (get ranks of the jih column of M, (ties are broken at random))
7: for = to n do
8: rij + R (get the rank of the äth element of the jth variable in the original data)
9: idæ Which(r, = rtyl) [tind which element the vector ry bas the same rank as Pey }
10: X +- M, M,(idr,) j] fassign corresoonding element M, rank matched matrix)
11: end for
12:
end for
13: Output: rank matched matrix X,
E. Additional Algorithms for the CategoricalSJPPDS Approach
Algorithm 1I describes how to create mapping between categorical variables and their (arbitrary) numeric rankings (which can then be used to create a numerical rank encoding of the categorical data). For the sake clarity, we will walk through the algorithm using the toy example in the main text, where we assume that the ith column of is given by X, (A, A, A, B, B, C, C,C.C.C).
16

---

TabSDS: Lightweight, Fully Non-Paramettie and Model Free Approach for Generating Synthetic Tabular Data
Algorithm 11 CalegoriialTooNuueriicKK
1: Input: categorical data matrix X
2: numuar <- NumberOfCollmns/
3: mapR +- ( (create empty map)
4: R + [.] (create empty matrix)
5: for i = 1 to neurverr do
6: levels + ExtractLevvls(XX5
{obtain levels of variable i}
7: tb - { il) {abtain level counts of variahle i)
8: curcounts + CumulativeSum(tt) (compute cumulative counts from the table counts)
9: numlevels Length
{obtain number levels)
tmp + [:] (create empty matrix store the mapping for variable }}
11:
for to numlevels do
12:
idæ= Which(X[, = levels(i]) (obtain the indexes records for which variable equals j}
13:
lowerbound + cumcounts []] - ccompute the lower bound for the numerical encoding of level for variable
14:
upperbound + cumcounts [ + 1] (compute the upper bound for the numerical encuding of level for variable i)
15:
nrseq + Sequence(lowerbounde upperbound) {create sequence of numeric rank values starting at lower bouud and ending upper-
bound)
Rlidæ, i] < RandonPPrrmutaiio((rrse] {assign randomly shuffled numeric rank values to the positions variable corresponding to lovel
17:
tmpli.] + [Levelsjj], lowerboundd upperbound! {store mapping level
18: end for
19:
mapR(i) < tmp {store the mapping for variable 1}
20:
end for
Output: mapping mapn: numerical rank encoding
From line 6 we have that X; has levels = [A, B, C). From line 7, the counts of each of these levels are 71,4 = 3, nB = 2, and nc = From line 8, the cumulative counts are cumcounls = [0, 3, 5, 9].
For I, we have: from line 12 that the indexes of the rows containing level A are idr [1,2, from line 13 that the lower-bound is from line 14 that the upper-bound is 3; from line 15 that the sequence of numeric rank values are given by [1, 3). (Hence, the mapping between level A and the numeric rankings is given by A (1,2,3}.) From line 16 we see that the algorithm first randomly shuffles the numeric rank values before assigning them to the positions containing the A level. This ensures that the algorithm is effectively using the "at random" method to break ties among identical values. In line 17 the algorithm is storing the mapping for the A level in the table format [level, lower- bound, upper- upper-bound], namely.
level A
lower bound upper bound
3
For j we have that: the indexes the rows containing level B are idr [4, 5] (line 12); the lower-bound is (line 13); the upper-bound is 5 (line 14); the sequence of numeric rank values is given by [4, 5). so that the mapping between level B and the numeric rankings is given by B 54,5} (line 15),
level
lower bound
upper bound
A
3
B
4
5
For = 3, we have that: the indexes of the rows containing level C are idr = [6, 7, 7,8, (line 12); the lower-bound is (line 13); the uoper-bound is (line 14); the sequence of numeric rank values given by [6, 7, 8, 9). so that the mapping between level C and the numeric rankings is given by B (6, 7, 8, 9) (line 15),
level
lower bound
upper bound
A
3
(8)
B
4
5
C
6
9
17

---

TabSDS: Lightweight, Fully Non- Pon-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Note that the above table (8) corresponds the ith element of mapR.
Algorithm 12 performs the reverse transformation and given numerical rank encoding matrix, R, and the same mapping created in Algorithm 11, it transforms back the numeric rank encodings to the corresponding categorical values. Essentially, for each categorical variable (column of R), the algorithm first reads in the levels of the variable stored in the map (line 6), and then for each of these levels, the algorithm finds the indexes of the elements within the lower and upper rank bounds of the variable level (line 9), and then assign that level to the matrix storing the categorical data (line 10).
Algorithm 12 Numeric' Caaegooricc,,, mapr)
1: Input: encoded numeric rank data matrix R; mapping mapR
2: numuar < NumberOICollmmss
3: X, 1 []] (ereate empty m
4: for = 1 to numvar do
5: map; <- mayn. ki] (grah map of variable
6: levels + ExtractL (xe fextract lovels of var. 8}
7: numnlevels + Length( {obtain oumber of levels]
8: for = to numlevels do
9: idæ <- Which(map, [ooerbound]] S R.(. map: mnapsupppehhound
[ohtain the indexes of the records)
X.(idr, a] < levels[j] (assign level j}
11: end for
12: end for
13: Output: categorical data X,
F. Arbitrary Numeric Rank Encodings Have no Impact in the CategoricalSJPPDS Algorithm
As described in the main text, numeric rank encodings generated by Algorithm 11 are necessarily arbitrary, since the levels of categorical variables have no intrinsic order, and distinct orderings generate distinct numerical rank encodings. This arbitrariness, however, does not affect the performance of the CategoricalSJPPDS approach because the same mapping used transform X to R is also used transform R back to X..
To illustrate this point we generate synthetic data from subset of 7 randomly selected variables from the Mushroom (MU) dataset using 2 distinct numeric rank encoding maps, mapR. and maPR.. The alternative rank encodings were obtained by modifying Algorithm 11 so that the order of variable levels obtained in line 6 is randomly shuffled.
For the rank encoding a, the modified algorithm generates a numeric rank encoding matrix R,, whose Pearson correlation matrix shown Figure 9a. For the alternative rank encoding b, the modified algorithm generates a numeric rank encoding matrix Rg. whose Pearson correlation matrix is shown Figure 9d.
Application of SJPPDS R., and R, generate, respectively, the shuffled numeric rank encoding matrices RØ and Ri whose correlation matrices are shown in Figures 9b and e, respectively.
Note that while the correlation structure of the numerical encoding matrices R., and R, are quite distinct (compare Figure 9a to 9d), the SJPPDS approach generates shuffled versions R and R, which closely approximate the association structures of the respective R,, and R., matrices (compare Figure 9a to and Figure 9d to 9e).
Application of Algorithm 12 to g and Rí generates synthetic categorical datasets X and X whose pairwise association matrices (computed using the Cramer-V V statistic) shown, respectively, in Figures 9c to 9f. (For comparison, Figure 10 shows the Cramer-V V matrix computed on the real data, illustrating that both numeric rank encodings generate similar statistical associations to the real categorical data.)
This example, illustrates that the choice of the numerical rank encoding used to transform the categorical data is immaterial.
18

---

TabSDS: Lightweight, Fully Non- Parametric, and Model Free Approach for Generating Synthetic Tabular Data
(a)
cor, encoding
(b))
cor. SJ PPDS encode
(C) -
Cramer encoding
8.8
3.8
2
2.8
244
24
0
02
6
(d)
cor. encoding
(e)
cor. SJ PPDS encode
Cramer V encoding
2
3
4
0.4
6
0.8
Figure 9. Performance of the CategoricalSIPPDS approach under alternative numerical rank encodings.
Hingagpe
aR-spiding
Drdkess 36
baget
kshape
target
84
ring Pype
slaring
-22
sakkesoorabove.ing
gllettachmmett
bruises 31
Figure 10. Pairwise association structure (as measure by the Cramer V statistic) computed on the real data for the randomly selected variables the Mushroom (MU) dataset. The association structure from synthetic data in Figure 9 and closely matches the association structure in the real data.
G. Extended Experimental Results Section
Experiments were based on 12 datasets described briefly in Table the main text. These datasets included 10 mixed datasets, 1 exclusively categorical dataset (Mushroom), and exclusively numerical dataset (California housing).
The Abalone (AB) and Adult (AD) datasets were fetched from openML using the Aeleam.datasedd module by calling,
from swwearn. datasets import fetch.openml
fetch [pech] "abaloee,",,,"" version=1, as frame=True) # Aba oone (AB)
fetch.openml (name- "adult", as.frame-True True, version-1) Adult (AD)
For the Adult dataset we removed rows containing missing values and recoded some of the variables (see code for details) as described in Hansen al. (2023).
19

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
The California housing (CH) dataset fetched using the command,
from sklearn, datasets import fetch
Eetch.califomriaahouusiioo (as (raem California housing (CH)
The Mushroom (MU) data was fetched using the openml package by calling,
openml datasets get_dataset (24) Mushroom (MU)
The Mushroom data was processed remove two columns prior the analysis ("stalk-root" which contained too many missing values, and "veil-type" which assumed the same value across all samples).
The remaining datasets were previously evaluated in Hansen et al. (2023). (The only two datasets from Hansen et al. which were not included in our comparisons were the Default and Heloc datasets which generated errors when evaluated with Synthcity's s Benchmarks function.) The datasets were fetched using the openml package by calling,
operml datasets get dataset (44126) Bank marketing (RM)
operml. tetatasets.get.dattttt (44089)
Credit (CR)
operml
(45022)
# Diabetes 130US (DT)
openml aaa.mmaattaastts.ee...ttttt.eee (44120)
# Electricity (EL)
openml @eeemmllattaaettt.ee..tttaeeee (44130)
4 Eye movements (EM)
operml www.sddaaatssssooooooo aaaamaa.tttattts.eeddaaaaaee (44123)
House 16H (HO)
operml
(44125)
Magic telescope (MT)
openml www.ddaattsss.... bee.aasets..et..daaaae... get.aatasddttttt..eee (44122)
# Pol
(PO)
G.1. Additional Comments on Baseline Model Selection
As pointed in the main text, restricted our comparisons to generators implemented in Synthcity. Some of the generators available in Synthcity were, nonetheless, excluded from our evaluations due to computational constrains. Preliminary checks showed it was unfeasible to include GReaT (Borisov et al., 2023), due to its heavy computational demands (we run our experiments in CPUs). (Also, recent work by Zhang et al. (2024) has shown that GReaT tends to be outperformed by DDPM, which is included in our comparisons.) We also excluded normalizing flows from our comparisons, as preliminary evaluations also showed was computationally more expensive than the other deep generative models. Finally, while the bayesian network generators does not represent a strong baseline, it was included in our comparisons an example of computationally efficient generator.
G.2. Hyperparameter Optimization for the Baseline Models
For the Abalone (AB). California housing (CH), and Mushroom (MU) datasets, the hyperparameter optimization for the DDPM, ARE, TVAE, and CTGAN baselines conducted in Syntheity using Optuna (Akiba et al., 2019) (over 20 trials for each model). The tuning process was guided by the minimization of the AUROC of XGBoost classifier trained to discriminate synthetic and real data. Tables 9, 10 and 11 report the optimized hyperparameter values for these three datasets.
The remaining datasets were evaluated in Hansen et al. (2023) and we adopted the same hyperparameter values employed in their paper for the DDPM, TVAE, and CTGAN models. These hyperparameters are reported in Supplementary Table in Hansen et al. (which also used Optuma guided by AUROC minimization of XGBoost classifier in their optimization). (The adoption of these published hyperparameter values allowed for considerable computation savings, given that the Optuna optimization was by far the most time consuming step in the experiments.) For the ARF baseline (which was not evaluated by Hansen et al.) we adopted the default values for the ARF plugin in Synthcity, which are close to the values used by Watson et al. 2023 in their experiments. Table 12 report the adopted hyperparameter values for these remaining datasets.
For the Nat baseline we adopted hill-climbing for structure search and BIC score for structure learning for all datasets. (Which corresponds to the values adopted by Hansen et al., 2023.)
20

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Table 9. Hyperparameters used for the generative models trained on the Abalone (AB) dataset.
Model
Parameters
7603
DDPM
(1002919988 19211227700001
buich sise: 970
suclasiiscation:
Jrees
ARF
delta: 0
stup: False
min nude. sine:
decoder a layers hidden:
weight docey: 0.001
batch.size: 128
docoder a units, hidden: 150
decoder_noulitt tosl
decoder dropout: 0.19944113331181166
encoder layers
encoder. nuuniss hidden: 100
encoder nedia reln
dropout: 0.01200245211222066
nJiir:
CTGAN
generator.n_lae sodocatorr.llyee.hhddeee
a.uniss hidden: hidden 100
penerator_noelin:
generalor dropoott: 1183662269984776666
discriminatur layers hidden:
discraminatrr
discriminatu
discrimnator.nn .nlierr
discraminator Arrpout: 0.02290110099922791
0.001
butchasize: 200
enceder max clustens 8
Table 10. Hyperparameters used for the generative models trained on the California housing (CH) dataset.
Modal
Parameters
DDPM
lr: 0.009223300 botch, sioe: 3177
num_timestqps: 200
num, Ineos: 70 dolt:
ARF
early stop: True
mis mnie mndkesiieee 6
200
decoder layers hidden:
weight decay: 0.001
butch.size:
embedking:
decoder wat.sr.anniisssiie hidden: 300
decoder leaky zelu
decoder drupout: 0,336557605516665 encoder_a.layers
encoder units hidden: 400 encoder.aveliat tach
encoder.doopour 0.02703347766999722
CTGAN
gemeralor.n..e htw.ir.nn..ee..hhdeeeeee
generator piikiiiommmmmiiiiikiik 150
Jhiddn:
generator_nonlin:
gemerater..topee 0. 1.16666900013333699
diserimirator, Jt. Jngeen_hhdderr
discriminator hisden: 150
disriminattr.oooll
discriminator.. ji
discriminatorrrrroood 0.06002274552420555
Ir. 0.02
weight_decay: butch-sioe: 200
encuder. mas clustun:
21

---

TabSDS: Lightweight, Fully Non-Parametin and Model Free Approach for Generating Synthetic Tabular Data
Table 11. Hyperparameters used for the generative models trained the Mushroom (MU) dataset.
Paramctters
n_Jier 5127
DDPM
(8884661824119999
num, limeslpps:
s.clasiifiattio: True
100
mun fters
early Falke
nJleer:
TVAE
In: 0.001
decoder saaeeays.hhhddde weight decay: biech_sier: Lumiis.cmbelding: 150
decoder units hidden: 150
decoder
decodet.dropout: 0.119171196618311
encuder a layers hidden:
hidden:
cacoder.aotli::
encoder drupoat: 0.1600221992266267
n.lier: 700
generalior numiiss www...nnmmiiiiiddmm...
gemerator_monlii:: lral
generator jfrogout 03097334222274666
discriminatuur hidden:
diseriminottrr.n.mmo mumiiit Jikden:
discriminattrnnonlin tanh
discriminator.n.iii
discrimminatorrlngeeee
16440661266933155
0.001
weightalecay: 0.001
totch_size: 500
Table 12. Hyperparameters used for the generative models trained on the remaining datasets, namely, Adult (AD), Bank marketing (BM),
Credit (CR), Diabetes 130US (DI), Electricity (EL), Eye movements (EM), House 16H (HO), Magic telescope (MT), Mushroom (MU), and Pol (PO).
Model
Parumelets
B. nJoer: 1851
DDPM
1L00095750825-22677666
mum timestege:: 998
is classificatio: True
Jnnes:
max_iters: 10
enrly Thue min_eode__ixe
o .eee: 300
TVAE
Ir: 0,0002 decoder layes hidden: weight,dacay: butch size: 256
units enbedkingg 200
decoder_o. jiiden: 300
nonlin:
decnder dropout: 0. 19992519112266
encoder Jayers hidden:
encoder hidden 450
encoder_nonlin: reaa
encoder dropoutt 01428666708947118
1030
generator layers hödden:
mnnerato...units... hidden: 50
generator nonlim: tash
generalor drupout: 0.0575
discriminator.ac http://uwwo....aee.....ooooo
discriminator a units hidden: 150
discriminator.oooo monlmn: rolu
discriminator.a.
dropout:
Ir. 0.001
weightdeccay: 0.001
butch size: 200
22

---

TabSDS: Lightweight, Fully Non- Pan-marametric, and Model Free Approach for Generating Synthetic Tabular Data
G.3. The DBLR and SDID Metries and their Sorted Versions, SDBLR and SSDID
In our evaluations of experiment we adopted sorted versions of the following standard disclosure risk metrics in the statistical disclosure control field:
1. The Distance- Based Record Linkage (DBRL) metric (Pagliuca and Seri, 1999; Domingo- Ferrer and Torra, 2001) is widely used approach for assessing re-identification disclosure risk in Statistical Disclosure Control (SDC). The method calculates the Euclidean distance between each record in the masked dataset and all records in the original dataset. A masked record is considered "linked" if its closest match in the original dataset is its true, corresponding record. The DBRL metric is then defined as the proportion of masked records that are correctly linked to their original counterparts.
2.
The standard deviation interval distance (SDID) metric (MateoSanz, Sebe, and Domingo-Ferre, 2004) is a popular metric for measuring attribute disclosure risk. It corresponds to the proportion of original records inside a standard deviation interval whose center is the corresponding masked record (where the interval width is computed in terms of a percentage of the standard deviation the variable). A record in the original dataset is considered to be inside the standard deviation interval of masked record if, for all variables j. is inside the respective stand. dev. interval.
Strictly speaking, these two metries are only indicated to evaluate masking methods for which there exists a mapping between the original and masked values (such as when the masked data is generated by adding noise to the original data). For synthetic data (for which such mapping is unavailable) is still, nonetheless, possible to find an approximate mapping using an analogous strategy the ones adopted by Domingo-Fos Ferrer al. (2020) and Chaibub Neto (2024). Basically, an approximate mapping between the original and synthetic datasets is obtained by sorting the rows of both the original and synthetic datasets according to the values of given attribute (column) of the data, and then perform the metric computation on the sorted datasets. (A justification for this procedure is provided in section 3 of Domingo-Ferrer et al., 2020.) In our experiments we sorted the data according to the variable with largest number unique values. These sorted versions the DBRL and SDID metrics are denoted here as the SDBRL and SSDID metrics.
G.4. Illustration of the Influence of the n. Parameter on the Quality of the Synthetic Data Generated by TabSDS
Figure shows scatterplots of the Latitude versus Longitude variables in the California housing (CH) dataset (alongside the boundaries if the California state in black). In each panel, random sample of 1000 points is shown in blue for the real data and in red for the synthetic data generated by TabSDS. The blue and red lines represent the least squares fits to the real and synthetic data, respectively.
Panel shows that for ne 1, TabSDS is unable to preserve any of the association observed in the real data. (The horizontal red line indicates that the Latitude and Longitude variables are essentially uncorrelated.) However, as ne increases, TabSDS generates increasingly more realistic data, and already generates fairly realistic data for n. = 30.
c=l
(D)
[C)
c
synth
synth real
synth
40
real
800
real
36
Laboub x
8-
-124
-11
-124
-120
-136
-124
-120
-120
Longbude
Long
Longitude
(d)
n c 10
n. c 30
(
c 200
sy:th real
synth real
synth
Labuuk
3--
x-
-124
-.50
-144
-100
-116
-124
-120
-116
Longbude
Long
Longitude
Figure 11. Influence the n. parameter on the quality the synthetic data generated by TabSDS
23

---

TabSDS: Lightweight, Fully Non-Parametri and Model Free Approach for Generating Synthetic Tabular Data
G.S. Tuning Parameter Selection for TabSDS
As described in the main text, the ne tuning parameter from the TabSDS approach was selected from grid of 24 values. The adopted selection criterion the following. For datasets containing mostly categorical variables (namely, Adult and Mushroom), selected the largest ne value which balanced well the tradeoff between detection test, ML effficiency, and domias MIA. For the remaining datasets (which contain mostly numerical variables) we compared the DCR distributions from the synthetic data generated with increasing ne values against the DCR distribution of the test-set, and selected the largest Re value which generates a DCR distribution with a median value close to the median the test set DCR distribution.
Figures 12 to 23 report the following:
Panel shows the detection test metric (based on XGBoost classifier).
Panel b shows the MI efficiency metric (based XGBoost learner). The horizontal grey line reports the ground truth value (i.e., the predicted performance the (real) test set from learner trained on the (real) training set data).
Panel reports the domias MIA metric.
Panel d shows the DCR distributions between training and synthetic samples (white boxplots) and between training and test sets (grey boxplots).
Detection test, ML efficiency, and the domias MIA metrics were computed using Synthecity's 's Benchmarks function. For the domias MIA metric only used the "KDE" and "prior" density estimation methods the BNFA was computationally too expensive. For most datasets, the Benchmarks function only outputted the domias MIA metrics based on the prior knowledge method (and for the House 16H and Eye movement datasets, it failed to generate a MIA estimate). Additionally, for some datasets it generated MIA scores consistently lower than 0.5. Use of the considerably more expensive BNFA estimator in some preliminary tests did not resolve these issues. These observations suggest that computation the domias MIA metric can be challenging in some datasets, and results should be interpreted with caution. all Figures panels a, and report the average values across 10 replications.
Except for the Adult and Mushroom datasets (Figures 13 and 22), the ne values were selected by inspecting panel of the plots. In all plots the red dots highlight the metric values for the selected n. parameter, and Table 13 summarizes the results.
For the Adult dataset we selected n. = 20, which produced a detection test lower than 0.7, MI. efficiencies above 0.88, and domias MIA already above 0.76. For the Mushroom dataset we select ne = 40, which produced a detection test lower than 0.7, ML efficiencies above 0.99, and domias MIA around 0.64.
Table 13. Selected values.
DATASET
AB
AD 20
BM
CH
CR
DI
EL
EM
HO
MT
MU
PO
SELECTED ne
100
200
1000
35
20
1000
25
40
15
detection test
ML efficiency
Domias MIA
(d)
DCR distributions
0.55
0.25
0,90
0.20-
0.58
metri
metric
0.45
metric
0.15-
o 8
0.10-
0,54
0.05
0.35
0.00
0
200
600
1000
200
600
1000
200
600
1000
100
200
300
400-
500-
600
700-
800-
900
1000-
ne
Figure Tuning parameter selection for the Abalone (AB) dataset. Selected n. 20.
24

---

TabSDS: Lightweight, Fully Non-Paramettro and Model Free Approach for Generating Synthetic Tabular Data
detection test
(b)
ML efficiency
Domias MIA
0.850
09
0.30
0.7 0.3
0.880
metric
metric
metric
0,76
0.870
0.72
0.860
200
1000
200
600
1000
200
600
1000
fcc
n:
Fc
Figure 13. Tuning parameter selection for the Adult (AD) dataset. Selected ne 20.
detection test
(b)
ML efficiency
0,395
Domias MIA
100 (d)
DCR distributions
0.85
80-
0.385
metric
0.75
metric
0.75
60-
0.375
40
0.70
20
0.05
0.365
200
1000
200
600
1000
200
600
1000
60
20
80
100
200
301
600
500
600
700
800
900
1000-
nc
ng
Figure 14. Tuning parameter selection for the Bank marketing (BM) dataset. Selected 100.
detection test
(b) ML efficiency
Domias MIA
(d)
DCR distributions
0.80
0,90
00000
0.52
0.70
metre
0.80
metric
metri
0.48
DCR
0.50
0,70
0.44
0.50
200
600
1000
200
600
1000
200
600
1000
AV
30
25
80
100
200
400-
500
600
700
800
900
1000-
nc
Figure 15. Tuning parameter selection for the California housing (CH) dataset. Selected 200.
detection test
(b) ML efficiency
Domias MIA
(d)
DCR distributions
0.91
0.80
0.37
15-
0.89
metric
metric
0.36
DCR
10-
0.70
0,57
0.35
0.85
0.50
0.34
200
1000
200
600
1000
200
600
1000
60-
80
100-
500-1
600
700-
8007
900
1000-
ne
ng
ne
Figure 16. Tuning parameter selection for the Credit (CR) dataset. Selected 1000.
25

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
detection test
(b)
ML efficiency
Domias MIA
0
DCR distributions
0.62
o 0000000000000
0
0,68
2.5-
0.51
2.0-
metric
0,54
metric
0.58
51.
0.49
0,60
0.0
200
1000
200
600
1000
200
600
1000
60
90
10
200
500
600
700
800
900
1000
fc
n:
Fc
Figure 17. Tuning parameter selection for the Diabetes 130US (DI) dataset. Selected 35.
(a) detection test
(b) ML efficiency
Domias MIA
(d)
DCR distributions
0.12
000000000
0 0
0.90
0.95
0.10
0.52
0.08
metric
0.90
metric
0,80
006
0.85
0.50
0.02
0.70
0.00
200
1000
200
600
1000
200
600
1000
60
P0
80
90
100
200
300-
600-
500-
500-
700-
800-
900-
10000-
nc
ng
n
Figure 18. Tuning parameter selection for the Electricity (EI.) dataset. Selected = 20.
1,00
(a)
detection test
0.84
(b) ML efficiency
domias MIA
(d)
DCR distributions
500-
400
metti
metric
0.60
metric
5000
200
0.70
0.56
100
200
600
1000
200
600
1000
80
100
200
500
500
700-
800
900
1000-
nc
n;
Figure 19. Tuning parameter selection for the Eye movements (EM) dataset. Selected ni 20.
(a)
detection test
(b) ML efficiency
(C) domias MIA
(d)
DCR distributions
0.94
00000000 o
0.05
0.90
metric
metric
DCR
0.35
0.86
0.82
200
1000
200
600
1000
60-
80
200
400-
500
600
700-
800--
900
1000-
nc
ng
Re
Figure 20. Tuning parameter selection for the House 16H (HO) dataset. Selected n. 1000.
26

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
detection test
(b)
ML efficiency
Domias MIA
0
DCR distributions
0.92
0.41
50-
metric
metric
0,88
metric
0.39
DCR
30
0.7
20
000000
10-
0.84
0.37
200
1000
200
600
1000
200
600
1000
10
600
700
800
900
1000-
ncc
n:
nc
Figure 21. Tuning parameter selection for the Magic telescope (MT) dataset. Selected 25.
detection test
(b) ML efficiency
Domias MIA
0000000000000
0.66
0.9
0.99995
08
0.62
metric
metric
06 0.7
0.58
0.9985
0.54
0.
200
600
1000
200
600
1000
200
600
1000
nc
Figure Tuning parameter selection Mushroom (MU) dataset. Selected n.,
[a]
detection test
(b) ML efficiency
Domias MIA
d
DCR distributions
40-
0.990
30-
metile
0,90
metric
0,980
mettic
0.780
8 68
8 20
10-
0,80
0.970
0.770
-
300- 14
200
600
1000
200
600
1000
200
600
1000
30
35
40
A5
50
60
70
80
90
100
400
500
600
700-
1900
500-1
1000-
Figure 23. Tuning parameter selection for the Pol (PO) dataset. Selected me = 15.
27

---

TabSDS: Lightweight, Fully Non-Paramctric, and Model Free Approach for Generating Synthetic Tabular Data
G.6. Extended Results for Experiment Set
Here, we present extended results for experiment set 2. In addition to reporting the comparisons for the 10 datasets (which contain mostly numerical variables), these extended results also present comparisons against new baselines including: (i) SMOTE (Chawla et al., 2002), based on 5 and 20 nearest neighbors; (ii) two differential privacy (DP) methods. ADSGAN (Yoon et al., 2020) and PATEGAN (Jordon et al., 2019); and (iii) a simple additive noise perturbation method (Brand, 2004).
Noise addition was evaluated over a grid of 13 increasing levels of additive noise ranging from 1 1% to 50% of the standard deviation of each variable. The results for the DP-based models were based on default hyperparameter choices (and should, therefore, be taken with a grain of salt). SMOTE was evaluated using two number of neighbors tuning parameter values, k = and k 20 (and implemented for numerical variables alone).
Figures 24 and 25 report the comparisons between TabSDS and all the remaining baselines, except for the additive noise perturbation method (whose comparisons are presented in Figures 26 and 27). All figures report the tradeoff between data privacy (measured by DCR, SDBRL, and SSDID) and data fidelity (measured by the detection test AUC score).
The left panels (a, d. g. j, and m) on Figures 24 and 25 show DCR vs AUC plots. The red line represents the DCR score comparing the training and test sets and provides an estimate of the DCR value we would expect to see for an ideal generator able to draw i.i.d. data from the same distribution as the training data. The red dot represents the selected value of ne based on the DCR criterium (i.e., the DCR value closest to the test set DCR). The middle (b, e, h, k, and n) and right (c, f, i, I, and o) panels show the tradeoff plots comparing SDBRL AUC and SSDID vs AUC, respectively.
Overall, DDPM, TabSDS, and SMOTE tended to outperform the other methods in terms of fidelity (measured by the detection test AUC). These methods tended to show somewhat balanced performances with none of the methods consistently outperforming the others. However, in terms of privacy, SMOTE tended to be considerably worse than DDPM and TabSDS with respect to DCR. It also tended to be worse than DDPM (and of TabSDS to a lesser extent) in terms of DBRL and SDID,
ADSGAN, PATEGAN, TVAE, CTGAN, and BayesNet tended to trade high data privacy by low data fidelity. In all datasets, these methods showed AUCs close to 1, low SDBRL and SSDID, and high DCR. (These high DCR values are likely consequence that these models fail to approximate well the distribution of the training data.) ARF tended to do slightly better than these models in few datasets.
Figures 26 and 27 present the tradeoff curves comparing TabSDS (black) vs additive noise (blue). The additive noise approach showed high AUC values across all noise levels across most datasets and not competitive against TabSDS
In order to evaluate the impact of generating new values for numerical variables to improve privacy protection, also compare TabSDS against simplified version of the algorithm (denoted TabSJPPDS), which discards the new value generation step. Figures 28 and 29 compare TabSDS against TabSJPPDS, and illustrate the additional privacy protection achieved by generating new values. (Note the higher DCR and lower SSDID scores. The differences were less clear cut for SDBRL).
The results described above (and in the main text) were based on DCR values computed on the original data scales. Categorical variables were me--oodee prior to DCR computation. (Note this should not cause issues given that the datasets contained only a few binary categorical variables. Datasets containing only mostly categorical variables such as Mushroom and Adult datasets were not evaluated given that noise addition can only be applied to numeric data.)
One potential caveat when variables have different scales is that distance by the wider range variables. To evaluate this potential issue, we also performed comparisons hased on DCR values computed on scaled data (Figures 30 and 31). These results show the same qualitative conclusions as before. The main quantitative difference was that the selected n. values tended to lower, leading to a decrease in fidelity and increase in privacy of TabSDS relative to the previous results.
metrics (such as DCR) might be dominated
28

---

TabSDS: Lightweight, Fully Non-Parannn Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Abalone (AB)
Abalone (AB)
Abalone (AB)
1.00
Dotection test AUC (smaleer beterr
X
Detection (smaller, boter
Detection test AUC (smaleer, beteer
TabS DS
Ta
1n
DDPM
0.90
TVAE
CTGAN
ER
FN
BayesNet
0,90
ADSGAN
PATEGAN
70
SMOTE K2D
SMOTE
300
0.70
0.70
0.00
0.10
0.20
0.30
0.00
0.10
0.20
0.30
0.00
0.05
0.10
0:15
0.20
Disclosure risk SDBRL (smaller: bettarl
Disclosure risk SSDID (smaller: better)
Bank marketing (BM)
Bank marketing (B (M))
Bank marketing (BM)
Ditection test AUC (smaler beitrr)
V
Detection best AUC (smoler, beter)
Detection test AUC (smwler beter
0.95
9
0.85
0.75
6.75
100
00
1000
0.6
8
1000
0
15
20
25
30
35
40
0.00
0.01
0.02
0.03
0.000
0.005
0.010
0.015
Disciosure SDBRL (smailer, better
Disclosure risk S5DID (smaller: better)
California housing (CH)
Califormia housing (CH)
California housing (CH)
Ditection best AUC (smaller, better
14
Detection test AUC (smaller, better
1.0
Detection test AUC (smaller, better
oot o ago oW0
0.
0.9
0.9
50
100
n_c
0,8
00
100
0.8
100
6-
0.7
300
0-
1000
0.6
0.000
0.004
0.008
0.012
0.000
0.002
0.004
DCR
Disciosure
SDBRL (smaller. betterl
Disclosure risk SSDID (smaller. better)
Credit (CR)
k
Credit (CR)
Credit (CR)
1,00
Detection bect AUC (smaler, beitar)
Delection best AUC (srvlerr bette)
Derection test AUC (smwlter betwr)
0:95
0.95
0:90
70
n_c
20
D.c
0a5
1000
0as
1000
0,85
0:
0.00
0.00
6
10
0.000
0.002
0.004
0.006 0.008
0.0000
0.0004
0.0008
0.0012
Disclosure (smaller. better!
Disclosure risk S5DID (smailer, better)
Diabetes 130US (DI)
Diabetes 130US (DI)
Diabetes 130US (DI)
Ditlection test AUC (smaller, bateer
Detection test AUC (smaller better
Dettertic test AUC (smaller, better
-0
0.9
0.
0.8
D_c
0-
0.7
0.7
O-O
15
400
0.5
400
0
500
0.0
02
0.4
0.6
0.8
1.0
1.2
1.
0.001
0. 0.002
0.003
0.004
0.0000
0.0010
0.0020
0.0030
Disclosure risk DBBLL (smaller, better!
Disclosure risk S55 DID (smaller. better)
Figure 24, Privacy/utilityy tradcoff comparisons. See legend on panel a.
29

---

TabSDS: Lightweight, Fully Non-Paramin Paraaetamttiic, and Model Free Approach for Generating Synthetic Tabular Data
Electricity (EL)
1.00
Electricity (EL)
Electricity
Ditection test AUC (smalee, betert
Detection AUC. (smaller, boteet
Detection test AUC (smaller, betert
annioo ooog
0.95
40
0.95
200
200
200
0.90
TebSDS
0.90
DS
DDPN
400
n_c
400
n_c
ARF
0.85
TYRE
CTGAN
1000
Dayesflet
0,00
0.00
ADSGAN
PATEGAN
SHOTE K20
0,75
0,75
SHOTE KS
0.00
0.01
0:02
0.03 DCR
0.04
0.05
0.00
0.01
0.02
0.03
0.04
0.00
0.01
0.02
0.03
Disclosure risk SDBRL (smaller. bettarl
Disclosure risk SSDID (smaller: better)
Eye movement (EM)
Eye movement (EM)
Eye movement (EM)
1,00
Datection bect AUC (smaler, betar)
Detsect best (smater, beter)
Detection test AUC (smwter. betwr
FR
0.90
FR
8
n_e
D.c
0,00
60
8.0
0,70
800
800
100
200
300
400
500
0.00
0.55
0.10
0.15 0.20
0.25
0.00
0.05
0.10
0.11
Disciosure
(smaller, better!
Disclosure risk (smaller, better)
House 16H (HO)
House 16H (HO)
House 16H (HO)
1.00
Dateccion bext AUC (smalles bateer
Detection AUC (smaller, better
Detection test AUC (smaller, better
ooosi 8go
15
15
0.95
40
0.90
30
90
n_c
200
B_c
0,85
0
T1
500
0,80
500
1000 500
0.75
1000
075
1000
0.75
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.00
0.02
0.04
0.06
0.00
0.01
0.02 0.03
0.04
0:05
DCR
Disclosure risk SDBRL (smaller. betterl
Disclosure risk SSDID (smaller, better)
Magic telescope (MT)
Magic telescope (MT)
Magic telescope (MT)
Datection tect AUC (smaler, beiter)
80
Detection best AUC (snaler bette)
1.0
Denection AUC (smwter, beter
15 10
0,9
10
08
n_c
0,7
0.7
0000
35
06
0.6
0.6
50
0000
900
0.5
960
10
15
20
0.00
0.02
0.04
0.06
0.08
0.00
0.02
0.04
0.06
Disclosure
(smaller, better!
Disclosure risk
better)
Pol (PO)
Pol (PO)
Pol (PO)
1.00
Detection test AUC (smalee, better
X
Detection test (smaller, better
Detection test AUC (smwller, better
0.95
0,95
d8 0000 o
00000
0,90
0.90
0,90
L.C
8
60
60
0.85
0,05
80
8
0.80
0.80
0
800
10
20
0.000
0.010
0.020
0.030
0.000
0.004
0.008
Disclosure risk DBRL (smaller, better!
Disclosure risk SSDID (smaller: better)
Figure 25, Privacy/utilitty tradcoff comparisons. See legend on panel a.
30

---

TabSDS: Lightweight, Fully Non- Parametriiiiic and Model Free Approach for Generating Synthetic Tabular Data
Abalone (AB)
1.00
Abalone (AB)
Abalone (AB)
Ditecction test AUC (smaller, beterr
60 Rg0 9.000000-00000 0-0000000000
Detection test AUC. (smaller, bether
Detection test AUC (smaller, beteer
0.90
n_c
-R
FR
RR
0,00
0000 00
300 70
DS grid
0 80
TabSOS grid Adellvv grid
DS grid Addiive noise grid
0,70
Addilve noise grid
0.70
300
0,70
10
0.0
022
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
DCR
Disciosure risk SDRL (smaller. betterl
Disclosure risk SSDID (smaller. better
Bank marketing (BM)
Bank marketing (BM)
Bank marketing (BM)
Datection tect AUC ismaler, beter)
coc0 o 080 800 2009
9.00
Detection best AUC (smollr, beter)
a00o 0-0
Detection test AUC (smwter. beter)
0.95
0.95
0.95
0,85
15
0.75
0,75
0.7
T5 noise grid
TabSOS grid
TabS DS Additiv noise grid
1000
0.65
grid
1000
1000
3000
5000
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
DCR
Disciosure risk (smailer, bettert
Disclosure risk SSDID (smaller. better)
California housing (CH)
h
California housing (CH)
California housing (CH)
Detlection test AUC (smaller, better
0000 aBo 0:000
Detectton test AUC (smaller, better
1,0
Detection test AUC (smaleer, better
1,0
CIDO 000
0.9
45
0.9
R_c
0,8
100
0,0
R_c
07
100000 0
300
0,7
300
0,7
00000 0 0
Addilvv noise grid
Ta DS grid
11
0.6
(0000
TabSOS grid Additve grid
1000
Tabs DS grid Addiive noise grid
100
200
300
400
500
600
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
DCR
Disclosure risk DBRL (smaller. betterl
Disclosure risk SSDID (smaller. better)
Credit (CR)
1,00
k
Credit (CR)
Credit (CR)
Datectionn test AUC (smater, betar)
0oco oop c0E0-00 0O0P
Detectiion best AUC (smater, bette)
Detection test AUC (smater. betwr
0.55
0.95
0.95
n_c
n_c
n.c
0.90
0.90
0.90
1000 35
TS
TabSOS grid Additive grid
TabS DS Addibve noise grid
noise grid
1000
0.05
2000
4000
6000
8000
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
Disclosure risk in (smaller, bettert
Disclosure risk S5DID (smaller, better)
Diabetes 130US (DI)
Diabetes 130US (DI)
Diabetes 130US (DI)
Ditlection test AUC (smaller, bether
000 0 DOoKB 000 100-00
Detection test AUC (smaller, better
1.0
Detection test AUC (smaller, bette)
0.
0,9
0.9
n_c
0.8
FLc
n_c
07
0,7
0.7
1000
15
TS grid
TabSDS grid
Tabs DS grid Addiive noise grid
0,6
Addilive noise grid
400
0,6
Addluve grid
400
0.6
400
100
150
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
DCR
Disclosure risk DBRL (smaller, better!
Disclosure risk SSDID (smaller. better)
Figure 26, Privacy/utility tradcoff comparisons of TabSDS vs additive noise.
31

---

TabSDS: Lightweight, Fully Non- Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Electricity (EL)
Electricity (EL)
Electricity (EL)
1.00
Ditlection best AUC (smaller, beterr
100-0 0 0000-00
Detecttonn AUC. (smaller, beteer
Detection AUC (smaller beteer
20
10
10
0.95
0.95
0.95
200
200
200
0.90
300
A_c
0.90
320
0.90
300
R_c
0.85
600
0.05
600
0,85
600
TS
TabSOS grid
Tab5 DS grid Addiive noise grid
Addluve noise
1000
grid
1000
0.0
0,2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
Disciosure risk DBRL (smaller bettarl
Disclosure risk SSDID (smaller: better)
Eye movement (EM)
1,00
Eye movement (EM)
Eye movement (EM)
Datectiin bect AUC (smalter betar)
00/000
30000-0
90-99-900 00-000 000
Detecction best AUC (smaler. beter)
cococo o oo 00-010000
000
Detection test AUC (smwter, betwr
0000
0.90
0.90
0,90
8
n_c
n_c
n.c
0,80
0,80
4
60
60
0,70
Ta
0,70
TabSOS grld
0.70
Tabs DS Addivve noise grid
noise grid
800
grid
800
10000
20000 30000
40000
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6 0.8
Disciosure
(smaller, bettert
Disclosure risk S5DID (smaller, better)
House 16H (HO)
House 16H (HO)
House 16H (HO)
0,90 0.95 1.00
Detection test AUC (smaller batter
000000 100000000 Gp
000
Detection test AUC (smaller better
GO O
Detection test AUC (smaller, beteer
15
0,00 0,95
0,95
40
90
90
0,90
200 90
200
R_c
200
R_c
0.85
0,05
00000
00000-00-0
0.50
300
0.80
500
500
DS
TabSOS grid
TabS DS grid
noise
1000
0.75
grid
1000
noise grid
500
1500
2500
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.6
0.8
DCR
Disciosure risk SDBRL (smaller. bettar
Disclosure risk SSDID (smaller. better)
Magic telescope (MT)
k
Magic telescope (MT)
Magic telescope (MT)
Datection bect AUC ismaler, beiter)
5
Detection best AUC (smoler, bette)
1.0
Denection test AUC (smwttr, beter
1,0
0000 000 0-9- 0 -0 CO0B
09
10
0.9
09
Q3
03
20
n_c
TLC
0.7
0.7
0,7
30
30
30
@00p 000
000
066
50
50
Ta noise grid
TabSOS grid
TabS DS
900
0.5
grio
900
0.5
noise grid
500
1500
2500
0.0
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
Disclosure risk
bettert
Disclosure risk SSDID (smaller, better)
Pol (PO)
Pol (PO)
Pol (PO)
1,00
Ditection test AUC (smalee, better
00 op o0 000 oop 000
Detection test (smaller, better
8
Detection test AUC (smaller, better
0.95
0,95
O 0
00000
0.90
0.90
0,30
F_c
C
60
8
0,25
0,85
0,05
8D
20
8
TS grid noise
0.90
TabSDS grid
Tabs DS grid Addiive noise grid
800
grid
800
500
1500
2500
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
DCR
Disclosure risk DBRL (smaller, better!
Disclosure risk SSDID (smaller. better)
Figure 27, Privacy/utility tradcoff comparisons of TabSDS vs additive noise.
32

---

TabSDS: Lightweight, Fully Non- Parametamtiiic and Model Free Approach for Generating Synthetic Tabular Data
Abalone (AB)
Abalone (AB)
Abalone (AB)
Ta TabS] PPDS
0:30
0.20
5DBRL
SSDID
DRC
0.04
0.10
TabSD5
TabSDS
0.00
9
8
8
0.00
Tau5] PPDS
TauS PPDS
200
400
600
800
1000
200
400
600
800
1000
0
200
400
600
800
1000
Bank marketing (BM)
e
Bank marketing (BM)
Bank marketing (BM)
TebSDS
PPDS
0.3
0,03
24
8
DRC
2-
SDBRI
0.02
SSDID
0.02
20
0.01
0.01
15
TabSDS
TabSDS
0.00
TaaS]
TabSJ
200
400
600
800
1000
200
400
600
800
1000
200
400
600
800
1000
C_
9_c
C_
California housing (CH)
h
Califormia housing (CH)
California housing (CH)
D5
PPDS
0,012
0.000
DRC
5DBRL
0.000
SSDID
0.004
0.004
0
Ta
Tab5 D5
0.000
Tab5]
Tab5 PPDS
200
400
600
800
1000
200
400
600
800
1000
200
400
600
800
1000
Credit (CR)
Credit (CR)
Credit (CR)
0,10
TabSDS
Tabs PPDS
0.008
DRC
SDeRU
0.006
SSDI
0.004
0.002
TabSD5
TauS Regg Rugg PA
Tao$ PPDS
200
400
600
800
1000
200
400
600
800
1000
200
400
600
800
1000
C_0
9_c
Diabetes 130US (DI)
Diabetes 130US (DI)
Diabetes 130US (DI)
0.004
0.04
Da
PPDS
0,003
0.003
DRC
5DBRL
SSDID
0,002
0,002
0.001
Ta
Tabs DS
Tau5]
PPDS
TabS] PPDS
200
400
600
800
1000
200
400
600
800
1000
0
200
400
600
800
1000
Figure 28. Privacy comparisons of TabSDS vs TabSIPPDS.
33

---

TabSDS: Lightweight, Fully Non- Parametriiiiic and Model Free Approach for Generating Synthetic Tabular Data
Electricity (EL)
Electricity (EL)
Electricity (EL)
Ta TabS]PPDS
0.04
D o D -e aag2
0.03
DRC
5DBRL
SSDID
0,02
0.02
0.02
0=8-8
0.01
0.11
0.1
TabSD5
TabS
0.00
0 - 8
8-
0.0
Tab5J PPDS
TabS]
200
400
600
800
1000
200
400
600
800
1000
0
200
400
600
800
1000
250
Eye movement (EM)
e
Eye movement (EM)
Eye movement (EM)
TabSDS
0.25
88- 00000 0 o
200
TabS) PPDS
0,20
0.20
150
DRC
sDeau
0:35
SSDID
0,10
0os
0.05
TabSDS
6
TadSD3
8=
8- 8
8-
0.00
TaaSJ
TabSJ
200
400
600
800
1000
200
400
600
800
1000
200
400
600
800
1000
C_c
9_c
House 16H (HO)
h
House 16H (HO)
House 16H (HO)
05505
0.06
9 - 9 9 9--
0.04
DRC
SDBRL
0.04
8
SSDID
0.8
0.02
0.02
0.7
Ta
Tab5
0.6
0.00
Tao5] PPDS
Tab5
200
400
600
800
1000
200
400
600
800
1000
200
400
600
800
1000
Magic telescope (MT)
Magic telescope (MT)
Magic telescope (MT)
0.08
0,00
TabSDS
TabS] PPDS
0.06
8-8-8 o
00000
SDBRL
SSDID>
DRC
10
0.04
0.04
1000
0,02
0.02
TabSDS
TauSDS
0.00
Taa$J
TabSJ
200
400
600
800
1000
200
400
600
800
1000
200
400
600
800
1000
T_c
n_c
n_c
Pol (PO)
Pol (PO)
Pol (PO)
Tabs
D5
Tab5 PPDS
0.03
0.03
DRC
5DBRL
0.02
55DD
0.02
0.01
0.01
0 0
Ta
TabS DS
0.00
Tau5] PPDS
TabS] PPDS
200
400
600
800
1000
200
400
600
800
1000
0
200
400
600
800
1000
Figure 29, Privacy comparisons of TabSDS vs TabSJPPDS.
34

---

TabSDS: Lightweight, Fully Non- Parametric, and Model Free Approach for Generating Synthetic Tabular Data
Abalone (AB)
Abalone (AB)
Abalone (AB)
1.00
Detlcttinn test AUC (smaleer betert
Detection test (smaller, boter
Detection test AUC (smaleer, beteer
10
sel Ta
0.90
DDPM
ARF
TVAE
CTGAN
RR
FN
BayesNet
0,90
ADSGAN
PATEGAN
70
70
SMOTE K20
SMOTE_
0.70
0.70
0.0
0.4
0.6
0.8
1.0
1.2
0.00
0.10
0.20
0.30
0.00
0.05
0.10
0:15
0.20
DCR
Disclosure risk SDBRL (smaller: bettarl
Disclosure risk SSDID (smaller: better)
Bank marketing
M)
Bank marketing (B (M))
Bank marketing (BM)
Datection tect AUC ismaler beitrr)
Ditection best AUC (smoler, beter)
Detection test AUC (smwler beter
0.95
0.95
0.85
C.c
6.3
0.75
1000
0.65
Q8
8
1000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.00
0.01
0.02
0.03
0.000
0.005
0.010
0.015
Disciosure SDBRL (smailer, better
Disclosure risk S5DID (smaller: better)
California housing (CH)
Califormia housing (CH)
California housing (CH)
Detlection test AUC (smaller, beteer
Detection AUC (smaller, better
1.0
Detection test AUC (smaller, better
to ago o
0-
00
0.9
0.9
50
de g
100
n_c
0.8
00
100
0.6
0000
100
0-
0.7
300
6-
980.00
1000
1000
0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.000
0.004
0.008
0.012
0.000
0.002
0.004
Disciosure risk SDBRL (smaller. betterl
Disclosure risk SSDID (smaller. better)
Credit (CR)
Credit (CR)
Credit (CR)
1,00
Datection bect AUC ismaler, beitar)
Delection best AUC (smoler, bette)
Derection test AUC (smwlte, beter
0.95
0:95
0.95
0:90
70
n_c
20
D.c
3000
0as
Po
1000
0,85
0.00
0.00
0.0
0.4
0.6
0.8
1.0
0.000
0.002 0.004
0.006 0.008
0.0000
0.0004
0.0008
0.0012
Disclosure (smaller. better!
Disclosure risk S5DID (smailer, better)
Diabetes 130US (DI)
Diabetes 130US (DI)
Diabetes 130US (DI)
Dillection test AUC (smaller, bateer
Dentecton test AUC (smaller better
Dettcctinn test AUC (smaller, better
0.9
0.
n_c
0.8
D_c
0-
0.7
400 15
0
0.5
00
0
500
0.00
0.10
0.20
0.30
0.001
0.002
0.003
0.004
0.0000
0.0010
0.0020
0.0030
DCR
Disciosure risk S SDBRL (smaller, better!
Disclosure risk SSDID (smaller. better)
Figure 30. Privacy/utility tradcoff comparisons (with scaled DCR), See legend on panel a.
35

---

TabSDS: Lightweight, Fully Non-Paramene ParrPaarmttiic, and Model Free Approach for Generating Synthetic Tabular Data
Electricity (EL)
1.00
Electricity (EL)
Electricity
Ditection text AUC (smalle, beterr
Detection AUC. (smaller, boteet
Detection test AUC (smaller, beteer
do
0.95
40
0.95
200
200
200
TabSDs
0.90
DS
6-00
ARF
DDPN
400
n_c
0.85
400
n_c
TYRE
CTGAN
1000
Dayesflet
0,00
0.00
ADSGAN
PATEGAN
SHOTE K20
0,75
0,75
49
SHOTE KS
0.1
0.2
0.00
0.01
0.02
0.03
0.04
0.00
0.01
0.02
0.03
DCR
Disclosure SDBRL (smaller. bettarl
Disclosure risk SSDID (smaller: better)
Eye movement (EM) M)
Eye movement (EM)
Eye movement (EM)
1,00
Dataction Dect AUC (smaler, bettrr
DQ
Detsect best (smaler, beter)
Detection test AUC (smwter. beter
0.00
ER
0.90
FR
8
nlc
D.c
0,00
60
6.70
0,70
800
800
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00
0.55
0.10
0.15 0.20
0.25
0.00
0.05
0.10
0.11
Disciosure
(smaller, better!
Disclosure risk (smaller, better)
House 16H (HO)
House 16H (HO)
House 16H (HO)
1.00
Detection best AUC (sralle better
Detection AUC (snaller, better
Detection test AUC (smaller, better
15
15
0.95
OOOO DOOD
40
0.00
0.90
8go
30
90
n_c
200
R_c
0,85
0
T1
0.0000
500
0,80
500
500
0,75
1000
075
1000
0.75
1000
80
0.5
1.0
1.5
0.00
0.02
0.04
0.06
0.00
0.01
0.02 0.03
0.04
0:05
Disclosure risk SDBRL (smaller: betterl
Disclosure risk SSDID (smaller, better)
Magic telescope (MT)
Magic telescope (MT)
Magic telescope (MT)
1.0
Ditection tect AUC (smaler, beiter)
Detection best (snaler betwe)
Denection AUC (smwter, betwr
10
088 0,9
10
6-
0,7
0
35
&
0.6
0.6
50
0.5
960
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.02
0.04
0.06
0.08
0.00
0.02
0.04
0.06
Disclosure
(smaller, better!
Disclosure risk
better)
Pol (PO)
Pol (PO)
Pol (PO)
1.00
Ditecction test AUC (smalee, better
Detection test (smaller, better
Detection test AUC (smwller, better
0.95
0,95
00og.
00000
0,90
0.90
0,90
FLC
8
50
60
0.85
0,05
000 d6
80
8
0.80
0 m0
800
0.0
0.5
1.0
1.5
2.0
0.000
0.010
0.020
0.030
0.000
0.004
0.008
DCR
Disclosure risk DBRL (smaller, better!
Disclosure risk SSDID (smaller: better)
Figure 31. Privacy/utility tradcoff comparisons (with scaled DCR). See legend on panel a.
36

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
G.7. Runtime Experiment Details
The runtime experiments report the average combined runtime for model training and data generation computed using the t timeit it Python module. (Results reported in seconds and the averages were based on 5 replications.) For each dataset, models were benchmarked using the respective optimized hyperparameter values. Experiments were conducted on C5. C5.2xlarge compute optimized AWS instance equipped with 8 (Intel Xeon Scalable processors or AMD EPYC processors). Hyperparameter optimization takes considerably more time and is not reported in these experiments.
G.8. Qualitative Comparisons
For the qualitative comparisons we investigate how well the synthetic data is able to recover the pairwise statistical associations observed in the real data, as well as, how well the synthetic data mimic the marginal distributions of the real data. This is done for generators in the experiment sets and 2.
For each of the 12 datasets in experiment set 1, we produce synthetic data using the TabSDS, DDPM, ARF, TVAE, CTGAN, and BayesNet generators (based on their selected tuning parameter values) and:
1. Compute the pairwise association matrices for each of the generated synthetic datasets, as well as, for the real data. Given that these datasets contain both numeric and categorical variables, we compute the pairwise associations between numerical variables using Pearson correlation and between categorical variables using the Cramer-V V statistic. For pairs of numeric and categorical variables we regress the numeric variable on the categorical one and use the square root of the R2 statistic coefficient if we replace the categorical variable for numeric one.)
measure of association. (Note that this measure reduces to the absolute value of the correlation
2. For each synthetic dataset we compute the absolute value of the differences between the synthetic and real data association matrices. These absolute differences are visualized in Figure 32, where columns represent the generators and rows the datasets. In this plot, darker colors represent larger discrepancies between real and synthetic data. Additionally, we computed the L.2 distance between the association matrices (12d), which is also reported in Figure 32,
3. For each dataset, we visualize the marginal distributions of the first 7 variables in the data. These marginal distributions are reported in Figures 34 to 45.
For experiment set 2, we perform similar comparisons on the 10 datasets comparing TabSDS against the SMOTE (with and = 20 neighboors), ADSGAN, and the PATEGAN generators. The absolute differences between association matrices comparisons are presented in Figure 33. The marginal distribution comparisons are reported in Figures 46 55.
Overall, the results show that the TabSDS approach tends to generate more realistic data than baseline generators. In terms of pairwise associations, Figures 32 and 33 show that it tended to produce association matrices which where closer to the real data association matrix. (Note the overall lighter color and lower 12d scores for TabSDS in comparison to the other generators. Note as well that the SMOTE baseline (Figure 33) also tended to recover well the association structure of the data.) In terms of marginal distributions, inspection of Figures 34 to 55 also show that TabSDS tended to generate more realistic marginal distributions than the other baselines.
Finally, we point out that while the inspection of pairwise associations is useful, is certainly not ideal as, sometimes, we can see similar correlations for fairly unrealistic data. As an illustration, consider Figure 56 which shows scatterplots of the Latitude versus Longitude data in the California housing (CH) dataset (alongside the boundaries if the CA state in black). In each panel, a random sample of 1000 points is shown in blue for the real data and in red for the synthetic data. The blue and red lines represent the least squares fits to the real and synthetic data, respectively. Note that the blue and red lines are not too far from each other for ARF, TVAE, and CTGAN generators, which indicates that the correlations computed on the synthetic data are not too far from the correlation observed in the real data. However, the scatterplots show that these generators are still producing fairly unrealistic data (i.e., outside the boundaries of the CA state). Only TabSDS and DDPM produce realistic looking data in this example.
37

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS, 12d 0.002
ddpm, 12d 0.078
arf, 12d
0.000
tvae, 12d 0.080
ctgan, 12d 0.004
bayesnet, 12d 0.445
Abalone (AB)
Abalone (AB)
Nbalome (18)
Aballone
Abelone
Abalooe
TabSDS, 12d 0.004
ddpm, 12d 0.005
arf, 12d 0.006
tvae, 12d 0.009
ctqan, 12d 0.005
bavesnet, 12d 0.006
Adut (AD)
Aduz (AD)
Adut (AD)
(AD)
Adut (AD)
Bark mark (BM)
TabSDS, 12d 0.000
Bark meakk (BM)
ddpm, 12d 0.002
Bark (BM)
arf, 12d 0.000
(BIM)
tvae, 12d 0.002
mrank. (BM)
ctgan, 12d 0.002
Bark markk (BM)
bayesnet, 12d 0.018
Cal taus (CH)
TabSDS, 12d 0.000
Cal hous, (CH)
ddpm, 12d 0.001
Cal hous. (CH)
arf, 12d 0.002
tvae, 12d 0.019
(CH)
ctgan, 12d 0.017
Credit Cal hous. (CH)
bayesnet, 12d 0.059
TabSDS, 12d 0.000
ddpm, 12d 0.044
arf, 12d 0.008
tvae, 12d 0.023
ctgan, 12d 0.048
bayesnet, 12d 0.058
Crestit (CR)
Credit (CR)
Credit (CR)
(CR)
TabSDS, 12d 0.000
ddpm, 12d 0.000
arf, 12d 0.000
tvae, 0.005
clqan, 0.002
bavesnet, 12d 0.010
Diabatos (DI)
Diobetos (DI)
Diebetes (DI)
Electtic. Diabates (DI)
Diebetes (DI)
TabSDS, 12d 0.001
ddpm, 12d 0.002
arf, 12d 0.000
tvae, 0.005
clgan, 0.003
bayesnet, 12d 0.059
Electtic (EL)
Eleceric (EL)
Electric: (EL)
Electric (EL)
TabSDS, 12d 0.000
ddpm, 12d 0.027
arf, 12d 0.004
tvae, 12d 0.006
ctgan, 12d 0.005
bayesnet, 12d 0.035
Eye new. (EM))
Eye meV. (EM)
Eye mov. (EM)
Eye (EM)
Eye meV. (EM)
Eye
House 16H (HO)
TabSDS, 12d 0.000
House 1GH (HD)
ddpm, 12d 0.023
House 18H (HO)
arf, 12d 0.002
House 1GH (HO)
tvae, 12d 0.007
House (HO)
ctgan, 12d 0.009
House 1GH (HO)
bayesnet, 12d 0.051
TabSDs, 12d 0.000
ddpm, 12d 0.005
arf, 0.001
tvae, 0.009
ctqan, 0.004
bavesnet, 12d 0.120
Magic tel. (MT)
Mage tel (MT)
Magic tel. (MT)
Magicc tel. (MT)
Mage (MT)
Magic tel (MT)
Mustvban (MLL)
TabSDS, 12d 0.018
Mushroom (MU)
ddpm, 12d 0.044
Mushroom (MU)
arf, 12d 0.004
Mustrraom (ML)
tvae, 0,021
Mustroam (MU)
clgan, 0.035
Mustroam (MU)
bayesnet, 12d 0.025
TabSDS, 12d 0.000
ddpm, 12d 0.101
arf, IZd 0.002
tvae, 0.006
clgan, 0.007
bayesnet, 12d 0.025
Pal (PO)
PatPo
Pol (PO)
Pol (PO)
pal (PO)
Polie PPO
Figure Absolute differences hetween association matrices experiment set
Darker values indicate stronger discrepancy between
the real and synthetic datasets. 12d indicates the 1.2 norm hetween real and synthetic association matrices. (12d 0 indicate value lower than 0.001.)
38

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS, 12d 0.002
SMOTE 5, 12d
0.003
SMOTE 20, 12d
0.004
ADSGAN, 12d
0.003
PATEGAN, 12d 0.471
Abatonn (AB)
Abatone (AB)
Abalone (AB)
Abstone (AB)
Ta 0.000
SMOTE 5, 12d 0.000
SMOTE 20, 12d 0.000
ADSGAN, 0.001
PATEGAN, 12d 0.017
Bank matk (BM)
(BM)
Berkk mank (BM)
Borkt mark (BM)
TabSDS, 12d 0.000
SMOTE 5, 12d = 0.000
SMOTE 20, 12d = 0.001
ADSGAN, 12d 0.018
PATEGAN, 12d 0.058
Cal hous (CH)
Cal. (CH)
Cel. hous (CH)
Cal. hous. (CH)
TabSDS, 0.000
SMOTE 12d 0.000
SMOTE 12d
ADSGAN, 0.046
PATEGAN, 12d 0.059
Creditt (CR)
Creait (CR)
Credit (CR)
Credit (CR)
TabSD5, 12d= 0.000
SMOTE 5, 12d = 0.000
SMOTE 20, 12d = 0.000
ADSGAN, 0.001
PATEGAN, 12d 0.006
Diibates (DI)
Dlabetes (DI
Disbctes (DI
Diebetee
TabSDS, I2d 0.001
SMOTE 5, 12d 0.000
SMOTE 20, 12d 0.000
ADSGAN, 12d 0.003
PATEGAN, 12d 0.027
Electtic (EL)
Electrrc (EL)
Electric (EL)
Electrcc (EL)
Eleetticc
TabSDS, 0.000
SMOTE 5, 12d 0.001
SMOTE 20, 12d 0.001
ADSGAN, 0.004
PATEGAN, 0.041
Eyo mav. (EM)
Eye (EM)
Eye maov (EM)
Eyc mov. (EM)
TabSDS, 12d 0.000
SMOTE 5, 12d = 0.000
SMOTE 20, 12d = 0.000
ADSGAN, 12d 0.004
PATEGAN, 12d 0.061
House 18H (HO)
House 38H (HO)
House 16H (HO)
House IGGH (HD)
TabSDS, 0.000
SMOTE 12d 0.000
SMOTE 12d 0.001
ADSGAN, 0.005
PATEGAN, 12d 0.068
Magic tol. (MT))
Magic tsl. (MT)
Megic tel. (MT)
Mogic tol. (MTT
tel
TabSDS, 12d 0.000
SMOTE 5, 12d = 0.000
SMOTE 20, 12d = 0.000
ADSGAN, 12d 0.006
PATEGAN, 12d NA
Pol (PO)
Pol (PO)
Pol(PO)
(PO(
Pol(PO)
Figure 33. Absolute differences hetween association matrices for experiment set Darker values indicate stronger discrepancy between the real and synthetic datasets. 12d indicates the 1.2 norm hetween real and synthetic association matrices. (12d 0 indicate value lower than 0.001.)
39

---

TabSDS: Lightweight, Fully Non- Parametamttiic and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
3.0
Synth real
3.0
Swnth real
3.0
Synth real
sn cal
ynth aal
3.0
wtth
dersity
density
density
real
1.
155
1.5
1.5
0.0
0.0
0.0
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.0
0.8
0.0
0.8
0.0
0.4
0.8
Length
Length
Length
Length
Length
Length
TabSDS
ddpm
tvae
ctgan
bayesnet
kynth
ynth real
ynth
Whth
ynth al
ynth
3
real
3
dersity
tal
density
3
dersity
3
eal
2
2
2
2
7
1
0.0
0.6
0.0
0.3
0.0
0.3
0.6
0.0
0.3
0.6
0.0
0.3
0.6
0.0
0.3
0.6
Diameter
Diameter
Diameter
Diameter
Diameter
Dlameter
TabSDS
ddpm
arf
tvae
15
ctgan
bayesnet
synth real
synth real
synth real
synth real
synth real
synth real
6
density
dereity
density
density
10
dersity
8
6
4
5n
2
0.0
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
Height
Height
Height
Height
Height
Height
TabSDS
ddpm
0.8
arf
tvae
ctyan
bayesnet
synth real
synth real
synth real
synth
0.8
synth real
synth
0.4
density
0.4
dersity
0.4
density
real
density
dersity
0.4
real
0.4
0.4
0.0
0.0
0.0
0.0
0.0
0.0
1.5
3.0
0.0
1.5
3.0
0.0
1.5
3.0
0.0
1.5
3.0
0.0
1.5
3.0
0.0
1.5
3.0
Whole, weight
Whole_ Whole_weight
Whole_ weightt
Whole_ weight
Whole_ weight
Whole weight
TabSDS
ddpm
arf
tvae
2.0
ctgan
bayesnet
synth real
synth real
synth real
synth real
synth real
synth real
10
1.0 Son Moosen
derssa 1.
density
density
1.0
dersity
1.0
10
0.0
00
00
00
00
0.0 0.5 1.0
0.0
0.5 1.0
0.0
0.5 1.0
0.0
0.5 1.0
0.0
0.5 1.0
0.0
0.5 1.0
Shucked weight TabSDS
Shucked weight
Shucked weight
Shucked weight
Shucked weight
Shucked, weight
ddpm
arf
tvae
ctgan
bayesnet
3.0
synth real
20
synth real
3.0
synth real
synth real
synth real
2.0 3.0
synth real
2.0
22 Sasu
dersity
densily
density
densiy
1.5
2
1.5
1.0
0
1.0
0.0
00
00
00
000
0.0
0.4
0.0
0.4
0.0
0.4
0.0
0.4
0.0
0.4
0.0
0.4
Viscera, weight
Viscera, weight
Viscera, Viscera__weight
Viscera, weight
Viscera, weight
Viscera weight
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
synth real
synth real
synth real
synth real
synth real
synth real
2.
20
censty
density
denssy
3.0 2.0
OT SRuDD
2
0
10
00
00
00
00
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
weight
Shell weight
Shell weight
weight
Shell weight
Shell weight
Figure 34. Subset of marginal distributions for the Abalone (AB) dataset. (Experiment set
40

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
tvae
ctgan
bayesnet
synth real
synth real
synth real
synth real
synth real
synth
3e-06
30 3e-06
dersity
3c-06
density
density
4e-06
density
3e-06
real
0c-000
0e-00
0e-00
0e-00
0r-00
1000000
1000000
1000000
1000000
1000000
1000000
fniwgt
frllgtt
fniwgt
fnilgt
fnllgt
fniwgt
TabSDS
ddpm
tvae
ctgan
bavesnet
0.4
synth
0.4
synth real
0.2 0.4
synth
synth
044
synth
0.4
synth
real
density
dersity
real
density
real
dessity
real
dersity
real
0.2
0.2
0.2
0.2
0.0
0.0
0.0
15
15
5
10
10
education.num
education.num
education.nuu
education.num
education.num
education.num
TabSDS
ddpm
tvae
ctgan
bavesnet
5000
synth
5000
synth
5000
synth real
5000
synth
5000
synth
real
trqqusse
real
frequeeccy
Requency
real
frequency
real
2000
2000
2000
200
2000
0
3
2
2
4
1
2
1
3
3
age
age
age
age
age
15000
TabSDS
15000
ddpm
frequency 15000
15000
tvae
15000
ctgan
15000
bayesnet
synth
synth
synth real
synth
synth
synth
real
frequency
real
frequency
real
real
frequenccy
real
5000
5000
5000
5000
5000
Federal-gov
WithouttpayyFeeee eederlllg
pahhou-payfederrl-ggoo
Without-payf sedyyeeeerllggoo Without-payf panoout-payeeeerl-ggooo Vithout-ayf-edrrllgov
Without-
workclass
workclass
workclass
workclass
workclass
workclass
TabSDS
8000
ddpm
arf
tvae
ctgan
bayesnet
6000
0000
6000
6000
6000
synth
frequency
al
froquency
al
al
Requeecc
aal
frequeency
al
3000
4000
0008
3000
200
10th
9th
10th 9th
10th
9th
10th 9th
10th
9th
10th
9th
education
education
education
education
education
education
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
10000
10000
10000
10000
10000
10000
Trequency
frequency
Resqueno 4000
frequency
frequeency 4000
4000
4000
4000
Married Single
Married Single
Married
Single
Married
Single
Married
Single
Married 5 Single marital.sttuus
marital.status
marital.saatu
manttal.satus
marital.status
marital.satus
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
2500
1000 2500
2500
2500
2500
th
2500
th
frequency 1000
trequency
frequency
Requency
feequeccy
1000
000
1000
100
Adm Adm-clerical
Sales
Adm-clerical
Sales
Adm-clerical
Sales
Adm-clerical
Sales
Adm-clerical
Sales
Adm-clerical
Sales
occupation
occupation
occupation
occupation
occupation
occupation
Figure 35. Subset of marginal distributions for the Adult (AD) dataset. (Experiment 1)

---

TabSDS: Lightweight, Fully Non-Param Parametriiiiic and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
tvae
ctgan
bayesnet
0.04
0.04
0.04
0.04
0.04
synth real
synth real
synth real
synth real
synth real
synth
denaty
dersity
density
density
density
real
0.02
0.02
0.02
0.02
0.02
0.00
0,00
0.00
0.00
0.00
0.00
20
100
60
100
60
100
20
60
100
20
60
100
20
100
V1
V1
V1
V1
V1
V1
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
synth
synth
synth
synth
Se
synth
synth
densioy
4e-04
real
denstty
4e-04
real
dersity
4e-04
real
density
6e-04
real
density
4e-04
real
dersity
40-04
real
0e-00
0e-00
0c+00
0e400
0e-00
0e-00
40000
40000
40000
40000
40000
40000
V6
V6
V6
V6
V6
V6
TabSDS
ddpm
arf
tvae
ctyan
bayesnet
0.04
0.04
0.04
0.06
0.04
synth real
synth
synth
synth
synth
synth
0.02
density
0.02
dersity
0.02
density
0.03
density
0.03
real
dersity
0.00
0.00
0.00
0,00
0,00
0.00
0.00
0
10
30
30
30
10
30
10
30
10
30
V10
V10
V10
V10
V10
V10
TabSDS
ddpm
arf
tvae
ctyan
bayesnet
synth
synth
synth real
synth
synth
synth
0.0015
real
density
0.0015
real
dersity
0.0015
density
real
dessity
0.0015
real
dersity
0.0015
real
0.0000
0,0000
0.0000
0.0000
00000
0.0000
2000
4000
2000
4000
0
2000
4000
0
2000
4000
0
2000
4000
2000
4000
V12
V12
V12
V12
V12
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.6
synth
0.5
synth real
0.6
synth real
synth
0.6
synth
0.6
synth
real
densty
dersity
density
0.4
real
density
real
dersity
real
07
0.3
0.3
0.3
0.3
0.0
0.0
0.0
0.0
0.0
0
20
40
0
20
40
20
40
20
40
20
40
20
40
V13
V13
V13
V13
V13
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.04
synth
synth
0.04
synth
synth
synth real
0.04
synth
real
denstty
0.02
real
dersity
real
density
0.8
real
density
0.020
density
real
0.02
0.02
0.02
0.00
0.00
0.00
0.0
0.000
0.00
400
800
400
800
400
800
400
800
0
400
800
0
400
800
V14
V14
V14
v14
V14
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
2.0
synth real
2.0
synth real
2.0
synth real
150
synth real
2.0
synth real
2.0
synth
densio
oensey
density
density
density
deruitt
real
1.
10
1.0
1.0
1.0
50
0.0
0.0
0.0
0.0
0.0
0
20
40
60
0
20
40
60
0
20
40
60
20
40
60
0
20
40
60
0
20
40
60
V15
V15
V15
Figure 36. Subset of marginal distributions for the Bank marketing (BM) dataset. (Experiment set 1)
42

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
tvae
ctgan
bayesnet
0.30
0.20
synth real
synth real
0.20
synth real
synth real
synth real
synth
0.10
dematty
0.15
dersio
0.10
density
0.2
density
0.15
density
0.15
real
0.00
0.00
0.00
0.00
0.00
5
10
15
5
15
15
5
10
15
Medlncc
Medinc
Medinc
Medlnnc
Medinc
Medlnc
TabSDS
ddpm
tvae
ctgan
bayesnet
0.030
0.030
0.055 0.030
ynth eal
synth eal
ynth eal
yynth
ynth
ynth eal
0.015
denstt
0,020
dersity
0.015
density
eal
density
0.02
eal
dersity
0.000
0.000
0.000
0.00
0.000
20
40
20
20
40
20
40
HouseAge
HouseAge
HouseAge
HouseAge
HouseAge
HouseAge
TabSDS
ddpm
tvae
ctgan
bayesnet
0.30
synth
0.30
synth
0.30
synth
0.4
synth real
synth
0.30
synth real
0.15
real
demsin
0.15
real
dereity
0.15
real
density
density
0.2
real
dersity
0.15
0.00
0.00
0,00
0.00
40
40
40
80
40
80
80
ooms
AveR ooms
AveR.ooms
ovemsoms
AveRooms
AveR
TabSDS
ddpm
tvae
ctyan
bayesnet
12
12
12
12
synth real
synth real
synth real
synth real
synth
synth real
60
dersity
8
dersity
density
10
dessity
real
dersity
8
4
20
30
0
20
30
0
10
20
30
10
30
10
20
30
10
20
30
AveBedrms
AveBedrms
AveBedrms
AveBedrms
AveBedrms
AveBedrms
TS
ddpm
arf
tvae
ctgan
bayesnet
synth
synth
synth real
synth
6e-04
synth
synth
denstty
4c-04
real
denstt
44-04
real
dersity
40-04
density
real
density
real
dersity
40-04
real
0e+00
0e-00
0e400
0e400
0e-00
0c-00
0
20000
20000
20000
20000
20000
20000
Population
Population
Populatioo
Population
Population
Population
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
2.0
20
2.0
2.0
2.0
2.0
synth
synth real
synth
synth
synth
synth
real
dersit
real
density
real
denety
real
dersity
real
1.0
10
1.0
1.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
0
200
500
0
200
500
0
200
500
200
500
200
500
200
500
AveOcccp
Ave0ccup
AveOccup
AveOccup
AveOccup
AveOccup
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.4
synth
0.2 0.4
synth
0.4
synth real
synth
0.4
synth
0.4
synth
real
densty
real
density
density 0.2
real
density
real
density
real
0.2
02
0.2
00
00
00
0
0.0
32
36
40
32
36
40
32
36
40
32
36
40
32
36
40
32
36
40
Latiude
Latitude
Latitude
Latitude
Latitude
Latiude
Figure 37. Subset of marginal distributions for the California housing (CH) dataset. (Experiment set
43

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
tvae
ctgan
bayesnet
synth real
synth real
synth real
synth real
synth real
synth real
dersity
3
density
dersity
2 3
0
10000
10000
10000
10000
10000
10000
TabSDS
ddpm
0,030
arf
tvae
ctgan
bavesnet
synth
synth
synth
synth
synth
synth
0.015
real
denstty
0.015
real
dersity
0.015
real
density
0.02
real
density
0,020
real
dersity
0.015
real
0.000
0009
0.000
0.000
0.000
60
100
20
60
100
20
60
100
20
60
100
100
100
age
age
age
age
age
age
TabSDS
ddpm
tvae
2.0
ctgan
bayesnet
synth
synth real
synth
synth
synth real
synth
real
density
dereity
real
density
real
density
dersity
real
1.0
1.0
1.0
1.0
0.0
0.0
0.0
0.0
0.0
0
80
80
80
40
80
40
40
terO/Time30.99Dem
htt.m/mmm....DDessSsSaa... ser ays
TabSDS
ddpm
arf
tvae
ctyan
bayesnet
synth
synth
synth
synth
synth
synth
10
real
dersity
6
real
dersity
6
real
density
real
dessity
6
real
dersity
6
real
4
2
2
0
0 10000
25000
10000
25000
10000
25000
10000
25000
10000
25000
10000
2500
DebtR atio
Debtil atoo
aeboR
DebtRatio
DebtR
DebtR
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.00015
0.00010
synth
0.00010
synth
0.00010
synth
synth
G00010
synth
0.00010
synth
real
densiyy
real
derse
real
density
real
real
dersity
real
0.00000
00000
0,00000
000000
0,00000
0e+00
6e+04
0e+00
6e+04
De-400
6e+004
0e+00
6e+04
0e++0
6e+04
De+00
6e+04
Monthlyincome
Monthlyincome
Manthlylncome
Monthlylncome
Monthlyincome
Monthlylncome
0.08
TabSDS
0.08
ddpm
0.08
arf
0.12
tvae
ctgan
0.08
bayesnet
synth
synth
synth
synth
synth
synth
0.04
real
densty
0.04
real
dersity
0.04
real
density
0.06
real
density
0.06
real
density
0.04
real
0.00
0.0
0.00
0.00
0.00
0.00
20
40
20
40
0
20
40
0
20
40
0
20
40
20
40
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.30
0.30
synth real
synth real
synth real
density 200
synth real
synth
synth real
30
densey
density
density
real
densiit
0.15
0.15
100
A0
10
0.00
0.00
0
40
80
40
80
0
40
80
0
40
80
0
40
80
40
80
NumberOrTimesS00Dayl
NumberOfT 900s9
NumberOrTimess90Daysl
NumberOtTimes900ayyl
NumberöfT Bnmbeer
Figure 38. Subset of marginal distributions for the Credit (CR) dataset. (Experiment
44

---

TabSDS: Lightweight, Fully Non- Parametrii and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.20
synth real
0.20
synth real
0.20
synth real
0.20
synth real
0.30
synth real
synth
0.10
denety
0.10
dersity
0.30
density
0.10
density
0.35
density
0,2
real
0.00
0,00
0.00
0.00
0.0
15
10
15
10
15
10
15
5
10
time_ in_ hospital
time_ hospital
time_ hospital
time_ ___________e hospital
time_ in_ iospitiaal
time, in_ hospital
TabSDS
ddpm
tvae
ctgan
bavesnet
synth
synth
synth real
synth
synth
synth
0.015
real
density
0.015
real
dereity
0.015
densit
real
density
0.015
real
dersity
0.015
real
0.000
0.000
0.000
0.000
0.000
0.000
40
140
40
140
40
80
140
0
80
140
80
140
40
80
140
num lab, procedures
num, Jab_ procedures
num, lab_ proccduuress
num, lab procedures
lab, procedures
num, lab ppo.ceddeeeess
0.06
TS
0,06
ddpm
0.06
tvae
ctgan
0.06
bayesnet
synth
synth real
synth real
0.06
synth
0.04 0.08
synth
synth real
density
0.03
real
density
0.03
dereity
0.03
density
real
density
real
dersity
0.03
0.03
0.00
0.00
0.00
0.00
0.00
0.00
20
60
20
20
60
0
20
60
medications
medications
num, medications
num medications tvae
num, medications
num medications
TabSDS
ddpm
ctgan
bayesnet
2.0
20
dessity 5000
800
synth real
synth real
synth
synth
synth real
synth real
dersity
real
density
10000
real
dersity
1.0
1.
2000
400
0.0
0.0
0
10
30
10
30
10
10
30
0
10
30
0
10
30
number_ outpatient
number_ _utpatient
number_ _ottratentt
number_outpatee outpatient
number_ outpatient number_outpatient
number_ outpatient
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
3.0
2.0
synth real
Aysuao
02
synth real
n Rensan de
real
synth
denslty 8000
synth real
demaeyy 5000
synth real
1500
synth real
1.0
00
Dr
4000
2000
deca 300
0.0
00
0.0
0
20
60
0
20
20
20
60
20
60
0
20
60
number_emmee e
number_ eebbbernyy
embrrgncc
number_ embrrgnyyy
number emergency
number_ eambberremrgeenyyy
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
3.0
30 oz O'
3.0
3.0
3.0
3.0
synth real
synth real
synth real
synth real
synth real
synth real
2.0
fysuso
Dr Desure
0z
Gessi
2.0
2.0
20
1.0
066 1.0
7.0
0.0
00
000
0.0
00
010
0
5
10
15
5
10
15
5
10
15
10
15
0
10
15
0
5
10
15
number_ Inpatient
number Inpatient
number Inpatient
number, Inpatient
number Inpatient
number inpatient
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
088
synth real
0.8
synth real
0.8
synth real
synth
0.8
synth real
08
synth real
densio
dersity
density
real
density
dentsty
0.4
04
0.4
04
0.4
00
00
0
0
00
10
15
0
10
15
0
5
10
15
0
5
10
15
0
5
10
15
5
10
15
number diagnoses
number diagnoses
number diagnoses
number diagnoses
number diagnoses
number, diagnoses
Figure 39. Subset of marginal distributions for the Diabetes 130US (DI) dataset. (Experiment set 1)
45

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
3.0
1.3 30
sy rea
3.0
3.0
th rea
3.0
2.0
real
dersio
2.0
re
Gensi
rea
density
2.0
dersino
1.0 2.0
1.0
1.0
1.0
0.0
00
0.0
00
0.0
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
date
date
date
date
date
date
Ta
ddpm
1.2
tvae
ctgan
bavesnet
densio
0.8
syrch real
demstty
0.8
real
dersity
0.8
rea
Sntth
density
1.5
1.0
synth teal
density
1.2
dersity
088
syrth
real
0.4
0.4
0.4
0.5
0.6
0.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.4
0.0
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
period
period
period
period
period
period
20
TabSDS
20
ddpm
20
25
tvae
20
ctyan
20
bayesnet
synth
synth
synth real
synth
synth real
synth
density
real
density
real
dersity
density
real
density
dersity
real
10
10
10
10
10
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
nnwiriiee
nswprice
nswprice
ns wppricee
nswprice
nswprice
3.0
TS
3.0
ddpm
3.0
arf
tvae
ctgan
3.0
bayesnet
3.0
synth real
synth
synth real
synth real
synth real
synth
2.0
23
real
dersity
2.0
density
dessity
2.0
dersity
2.0
real
2
1.0
10
1.0
1.0
1.0
0.0
00
0.0
0.0
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
nswdemand
nswdemand
nswdemand
nswdemann
nswdemand
nswdemand
2000
TS
2000
ddpm
20000
arf
2000
tvae
2000
ctgan
2000
bayesnet
synth real
synth real
synth
synth real
synth real
synth real
density
1000
1000
dera
1000
real
density
dleeeity
1000
dersity
1000
0.0
0.4
0.8
0.0
0.4
0.8
0.0
D.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
vicprice
vicprice
vicprice
vicprice
vicprice
vicprice
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
17
synth
5 10 15
synth real
15
synth real
synth real
15
synth real
10 15
synth real
10
real
densty
dersitt
10
density
density
10
density
5
5
5
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
vicdemand
vicdemand
vicdemand
vicdemand
vicdemand
vicdemand
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
synth
synth real
synth real
synth real
synth
synth real
6 8
10
real
densty
6
demsity
density
density
6
real
density
4
2
2
2
2
0
0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
transfer
transter
transfer
transter
transter
transfer
Figure 40. Subset of marginal distributions for the Electricity (EL) dataset. (Experiment set
46

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
arf
tvae
ctgan
bavesnet
density
6e-05
rea
denstty
0,00015
synth real
dersity
6c-05 -5-05
Synth
density
0.00008
density
0,00008
density
6e-05
rea
0c-00
0.00000
0e-00
0.00000
0.00000
00-00
-2000
6000
-2000
6000
-2000
6000
-22000
6000
-0000
6000
-2000
6000
lineNo
lineNo
lineNo
lineNo
lineNo
lineNo
TabSDS
0.008
ddpm
arf
tvae
ctgan
bavesnet
0.002 0.004
syrth
synth
synth
0.0020
density
0,004
rea
deriity
0.0020
density
real
density
dersity
0.002
0,0000
0.000
0.0000
0.000
0.000
200
400
200
400
200
400
200
400
200
400
200
400
assgNo
assgNo
assgNo
assgNo
assgNo
assgNo
TabSDS
ddpm
tvae
0.088
ctgan
bayesnet
0.005
0.006
0.006
synth
synth
synth
synth
synth
synth
density
0,003
real
density
0,003
real
dersity
0.003
real
density
real
density
0.001
real
dersity
0.004
real
0.000
0,000
0.000
0.000
0.000
0.000
400
800
400
800
400
800
0
400
800
0
400
800
400 800
prevFixDur
prevF ixDur
prevf ixDur
prevFixDur
prevF ixD
prevf ixDur
TabSDS
ddpm
tvae
ctyan
bayesnet
synth
synth
synth
synth real
synth
synth
0.004
real
Pensing
0.004
real
dersity
0.004
real
density
deseity
0.004
real
dersity
0.004
real
0.000
0000
0,000
0.000
0,00
0,000
400
800
400
B00
400
800
400
800
400
B00
0
400
800
firstrixDur
firstfiDDur
firstfiXDur
firstrxDur
firstfiDur
firstfixDur
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.003 0.006
synth
synth
synth
synth
synth real
synth
0.003
real
0.003
real
dersa
0.000
2003
real
density
real
density
dersity
0.003
real
0.000
0000
0000
0.000
0.000
0.000
400
1000
400
1000
400
1000
400
1000
0
400
1000
0
400
1000
firstP ass ixDur
firstPassF ixDur
firstP FisttP
firstP PrstPassFixDur
firstassFFixDa
firstP ass
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
synth
synth real
synth
synth
synth
synth real
density
0.004
real
0.004
real
density
0.006
real
deneity
0.005
real
deststy
0.004
Sase 1000
0.00
0.000
00000
0.000
0000
0.000
400
1000
400
1000
400
1000
0
400
1000
0
400
1000
0
400
1000
nextF ixDur
nextf ixDur
nextF ixDur
nextF Ixru
nextF IxDur
nextF
0.004
TabSDS
0.004
ddpm
0.004
arf
tvae
ctgan
0.004
bayesnet
synth
synth real
synth real
synth real
synth
synth
density
0.002
real
0.002
0012
density
Seneiyy
0.003
real
0.002
real
0.000
1000
0
0000
1000
0.00
0.000
500
1500
500
1500
0
500
1500
0
500
1500
0
500
1500
500
1500
firsts accLen
firstS accLen
firstaccLLen
first
firstSaccLen
firsta
Figure 41. Subset of marginal distributions for the Eye movements (EM) dataset. (Experiment 1)
47

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.00015
synth
0.00025
synth real
0.00015
synth real
0,00015
synth real
synth real
0.00020
synth
density
real
denarg
dersity
density
10000 0
dersity
real
0.00000
0,00000
g,00000
0.00000
1000000
0.00000
0e+00
4e+06
0e+00
4e+06
00++00
4e+06
0e+00
4e+06
0e+00
4e+06
0e+00
4e406
P1
P1
P1
P1
P1
P1
TabSDS
10 15 20
ddpm
20
arf
25
tvae
ctgan
bayesnet
15
synth
synth
synth real
synth
10 15
synth
10 15
synth
10
real
density
real
dersitty
density
15
real
density
real
dersity
real
5
5
0.2
0.4 0.6 0.8
0.2
0.4
0.8
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
P5p1
P P5p1
P5p1
P5p1
P5p1
P5p1
TabSDS
ddpm
tvae
ctgan
bayesnet
60
50
synth
synth
synth real
synth
synth
40
synth real
real
density
40
real
dersity 70
density
real
density
40
real
dersity
20
20
20
20
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0,4
0.8
0.0
0.4
0.8
P P6p2
P 6p2
P P6p2
P6p2
P6p2
P P692
TabSDS
ddpm
tvae
ctyan
bayesnet
10
synth real
synth real
synth real
synth real
synth real
synth real
dersitt
dersity
density
dessity
dersity
2
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
P11p4
P11p4
P11p4
P11p4
P11p4
P11p4
TSbSDS
ddpm
arf
tvae
ctgan
bayesnet
synth real
synth
synth real
synth
synth
synth real
denstyy
real
dersity
density
real
density
real
dersity
17
2
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
P14p9
P14p9
P14p9
P14p9
P14p9
P14p9
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
sy
sy
sy rep
h
sylth rea
sy
sy
rea
denseyy
rep
dlessityy
dencity
rgu
densiit
4
24
2
2
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
P15p1
P15p1
P15p1
P15p1
P15p1
P1pp1
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
8
synth real
80
synth real
80
synth real
synth real
synth
80
synth real
densty
density
density
density
real
deriiit
10
40
50
40
40
1
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
P15p3
P15p3
P15p3
P15p3
P15p3
P15p3
Figure 42, Subset of marginal distributions for the House 16H (HOO dataset. (Experiment set
48

---

TabSDS: Lightweight, Fully Non- Parametrii,, and Model Free Approach for Generating Synthetic Tabular Data
0.000
TabSDS
0,020
ddpm
0.020
tvae
0,030
ctgan
00,020
bayesnet
synth real
synth real
synth real
synth real
synth real
synth
0.010
denery
0.010
dersii
0,010
density
0.015
density
0.155
dersity
0.010
real
0.000
0.000
0.000
0.000
0.000
100
250
100
250
250
250
100
250
100
250
fLength.
fLength.
fLength.
fLength.
fLength.
fLength.
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.08
synth
synth
synth
synth real
synth real
synth
0.03
real
demsity
0,03
real
dersity
0.03
real
density
0.04
covalty
0.03
dersity
0.03
real
0.00
0.00
0.00
0.00
0.00
0.00
100
200
100
200
100
200
100
200
100
200
100
200
WWitth.
WWldth.
rWidth.
iWtth
WWidth.
fWidth.
TabSDS
ddpm
tvae
2.0
ctyan
bayesnet
0.8
synth
0.8
synth
synth
synth
synth
0.8
synth
real
denctty
real
dersity
real
density
real
density
real
dersity
real
1.0
0.4
0.4
0.6
0.4
0.0
0.0
0.0
0.0
0.0
2
5
5
4
3
2
5
ISize.
1S ize.
IS izee.
IS Iziz..
ize.
IS
TabSDS
ddpm
tvae
ctyan
bavesnet
2.0
2.0
2.0
2.0
2.0
synth
synth real
synth real
synth
synth real
synth real
real
dersity
dersity
density
real
dersity
dersity
1.0
1.0
1.0
1.0
1.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.4
0.B
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.B
0.0
0.4
0.8
0.0
0.4
0.8
fConc.
fConc.
onc.
fConc.
fConc.
fConc.
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
3.0
synth real
synth
3.0
synth real
synth real
synth real
3.0
synth
densiy
denshy
real
dersity
density
density
dersity
real
1.5
2
1.5
1.5
0.0
0.0
0.0
0.0
0.4
0.0
0.4
0.0
0.4
0.0
0.4
0.0
0.4
0.0
0.4
1Conc1.
fConc1.
(Concl.
fConc1.
fConc1.
fConc1.
0.012
TabSDS
tto
ddpm
0,012
arf
tvae
ctgan
0.02
bayesnet
synth
synth
synth real
synth real
synth
synth
densily
0.006
real
0,008
real
density
0.006
density
denett
0,0
real
density
0.005
real
0.000
0000
0,000
0.000
0000
0.000
-400
400
-400
0
400
-000
0
400
4000
0
400
-400
400
-400
400
fAsym.
fAsym.
sym.
fAsym.
fAsym.
sym
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
synth
synth real
synth real
synth
synth
synth real
0.010
real
densty
0,030
density
0,010
density
real
density
0.015
real
density
0.100
0.000
0.000
0.000
0.000
0.000
0.000
-300
0
200
-300
0
200
-300
200
-300
200
-300
0
200
-300
0
200
3Long
M33Logg.
IM3Long.
1M3Long.
IM3Long.
IM33
Figure 43. Subset of marginal distributions for the Magic telescope (MT) dataset. (Experiment set
49

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
1500
1500
1500
1500
1500
syn
sym
sym real
sym rea
sym real
syn real
frequency
rea
real
frequency
frequency
freqque
500
500
500
500
500
500
x
X
f
cap.shape
cap.shape ddpm
cap.shape
cap.shape
cap.shape
cap.shape
1500
TabSDS
froquuency 1500
1500
tvae
1500
ctgan
1500
bayesnet
1500
sym
frequency
rea
500
500
500
500
500
500
5
y
g
9
9
y
g
y
y
cap.surface
cap.surface
cap.surface
cap.surface
cap.surface
cap.surface
TabSDS
ddpm
tvae
ctgan
bayesnet
synth
synth real
synth
synth
synth
synth
hrqueecy
800
real
frequency
1000
froquency
800
real
Requency
real
frequency
800
real
frequeeccy
800
real
400
400
400
400
400
n
n
W
W
W
n
cap.color
cap.color
cap.color
cap.color
cap.color
cap.color
TabSDS
ddpm
tvae
ctgan
bavesnet
2000
synth
2000
synth
Reotas 200
synth
2000
synth
2000
synth
2000
synth
frequency
Prequency
frequeency
1000
1000
1000
1000
t
bruises.33
bFuises.3F
bruises.3F
bruises.33
bruises.3F
bruises.3F bayesnet
TabSDS
ddpm
tvae
ctgan
1500
synth
1500
synth
1500
Fynth
1500
synth
1500
kynth real
1900
Fynth
real
real
real
hrequenyy
real
real
500
500
5:00
500
500
m
y
m
m
p
P
y
m
V
odor
odor
odor
odor
TabSDS
ddpm
arf
4000
tvae
ctgan
bayesnet
frequency
troqusen
frequency
rrequency
frequuency
2000
2000
2000
2000
2000
à
à
gill. attachment
cll.attachment
gillattachment
gll.attachment
gillattachment
gillattachment bayesnet
TabSDS
ddpm
arf
tvae
ctgan
2500
synth
2500
synth
1000 2500
synth
2500
synth
2500
synth
2500
synth
real
frequency
real
frequency
real
frequency
real
mequeecy
real
frequency 1000
real
1000
1030
1630
W
w
w
W
C
gill.spacing
gil.spacing
gil.spacing
gill.paccng
gil.spacing
gill.spacing
Figure 44, Subset of marginal distributions for the Mushroom (MU) dataset. (Experiment
50

---

TabSDS: Lightweight, Fully Non-Paramens Parametric,,, and Model Free Approach for Generating Synthetic Tabular Data
0.020
TabSDS
0,020
ddpm
0,020
tvae
ctgan
0.020
bayesnet
0,020
synth real
synth real
synth real
synth real
synth real
synth real
0.010
0,010
dersity
0.010
density
density
0.015
dersity
0.010
0.000
0.000
0.000
0.000
0.000
0.000
150
150
50
150
50
50
150
150
15
15
15
f5
0.06
TabSDS
ddpm
0.06
arf
0.06
tvae
0.06
ctgan
0.06
bayesnet
synth
synth real
synth real
synth
synth
synth
0.03
real
demsity
0.04
dersity
0.03
density
0.03
real
density
0.03
real
dersity
0.03
real
0.00
0,00
0.00
0.00
0.00
80
140
200
140
200
140
200
140
200
80
140
200
80
140
200
16
f6
16
f6
TabSDS
ddpm
1.5
arf
tvae
ctgan
bayesnet
0.5
synth
0.6
synth real
synth real
synth
synth
0.6
synth
0.4
real
demoio
0.4
dersity
3.0
density
0.4
real
density
0.8
real
dersity
0.4
real
0.2
0.2
0.5
0.2
0.0
0.0
0.0
0.0
120
180
80
120
180
80
120
180
80
120
180
80
120
180
80
120
180
17
17
17
1.5
TabSDS
15
ddpm
tvae
1.5
ctyan
bayesnet
synth real
synth real
synth real
synth
synth
1.5
synth
1.0
dersity
1.0
demsity
density
real
density
1.0
real
dersity
1.0
real
0.5
0.5
0.5
0.5
0.5
0.0
0.0
0.0
0.0
0.0
80
120
180
80
120
180
80
120
180
120
180
80
120
180
80
120
180
18
f8
f8
0.30
TabSDS
0.30
ddpm
arf
tvae
ctgan
bayesnet
25
30
synth
synth real
0.4
synth real
synth real
synth real
synth
0.15
real
densiy
0.15
dersity
density
density
15
dersity
20
real
0.2
10
0.00
0.0
0.0
100
140
100
140
100
1440
100
140
100
140
100
1440
19
f9
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.8
synth real
0.8
synth real
0.8
synth real
1.2
synth real
1.2
synth real
0.8
synth
denssty
dersity
density
density
density
real
0.4
0.4
0.6
0.6
0.4
0.0
0.0
0.0
0.0
0.0
0
40
80
0
40
80
40
80
40
80
40
80
0
40
80
f13
f13
f13
f13
TabSDS
ddpm
arf
tvae
ctgan
bayesnet
0.08
synth real
0.08
synth
0.08
synth real
synth real
synth real
synth
densio
densty
real
density
density
0.10
density
0.06
densiiy
0.06
real
0.04
0.04
0.04
0.00
0.00
0,00
0.00
0.00
0.00
0
40
80
120
0
40
80
120
0
40
80
120
0
40
80
120
40
80
120
40
80
120
114
Figure 45. Subset of marginal distributions for the Pol (PO) dataset. (Experiment set
51

---

TabSDS: Lightweight, Fully Non- Con-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
3.0
synth real
3.0
synth real
3
synth real
synth real
3.0
synth
denoity
density
density
densily
eal
1.
7
12333
1.5
1
0.0
1
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.0
0.4
0.8
0.0
0.4
0.8
Length
Length
Length
Length
Length
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth real
Synth
real
dersity
real
dersity
real
densty
dersiby
m
eal
2
2
2
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
Diameter
Diameter
Diameter
Diameter
Diameter
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
12
synth
synth
synth real
synth
synth
6
real
dereity
real
dersity
6
8
densty
real
dersity
6
real
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.B
0.0
0.4
0.8
Height
Height
Height
Height
Height
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
0.8
synth real
synth
0.4
real
dereity
0.4
real
dersity
0.4
real
densiyy
dersity
0.4
real
0.4
0.0
0.0
0.0
0.0
1.0
2.0
3.0
0.0
1.0
2.0
3.0
0.0
1.0
2.0
3.0
0.0
1.0
2.0
3.0
0.0
1.0
2.0
3.0
Whole_ weight
Whole, weight
Whole weight
Whole weight
Whole weight
Ta
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth real
synth
synth
2.0
synth
synth real
10
dereiit
real
dersity
1.0
real
denstty
real
dersity
1.0
100
0.0
0.0
0.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
Shucked weight
Shucked
weight
Shucked weight
Shucked weight
Shucked weight
DS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
3.0
synth real
3.0
synth
3.0
synth
synth
3.0
synth real
2.0
denetty
real
density
real
denstyy
2 3
real
dersity
1.0 2.0
1.5
1.0
0.0
0.0
0.0 0.2 0.4 0.6
0.0
0.2 0.4 0.6
0.0
0.2
0.4 0.6
0.0
0.2
0.4 0.6
0.0 0.2 0.4 0.6
Viscera_ Viscera_weiiht
Viscera, weight
Viscera, weight
Viscera _eight
Viscera, weight
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
2.0
synth real
deretty
synth
real
dersity
2.0
real
synth
deneity
30
synth real
dersity
synth real
1.
1.0
1.5
1.0
0.0
0.0
0.0
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
Shell weight
Shell_ weight
Shell weight
Shell Whel__eelhh weight
Shell weight
Figure 46. Subset of marginal distributions for the Abalone (AB) dataset. (Experiment set
52

---

TabSDS: Lightweight, Fully Non- Con-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.04
0.04
0.04
synth real
0.04
synth real
synth real
0.04
synth real
synth
denclyy
density
density
dersity
real
0.02
0.02
0.02
0,02
0.02
0.00
0,00
0.00
0.00
0.00
20
80
20
40
60
20
60
80
20
40
40
60
80
V1
V1
V1
V1
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
4e-04
real
dereity
44-04
real
dersity
4e-04
real
densty
6e-04
real
dersity
real
0e+00
De+00
0c+00
0e400
40000
80000
40000
80000
40000
B0000
0
40000
80000
40000
8000C
V6
V6
V6
V6
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.04
0.06
synth real
0.04
synth real
0.04
synth real
synth
0.04
yntth
dereity
dersity
densiyy
real
dersity
eal
0.02
0.03
0.02
0.00
0.00
0.00
0.00
10
30
0
20
30
10
20
30
0
10
20
30
10
20
30
V10
V10
V10
V10
V10
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.0015
real
synth
dereity
synth
real
dersity
0.0015
real
synth
density
0,0020
synth
real
dersity
0.00155
real
synth
0.0000
0.0000
0.0000
0,0000
0.0000
0
1000
3000
0.
1000
3000
1000
3000
0
1000
3000
1000
3000
V12
V12
V12
V12
TabS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
06
synth
0.6
synth
0.6
synth
0.5
synth
synth
real
dereity
real
dersity
real
denstty
real
dersity
real
07
0.3
0.3
0.6
0.0
0.0
0.0
0
10
20
30
40
10
20
30
40
0
10
20
30
40
0
10
20
30
40
10
20
30
40
V13
V13
V13
V13
TabSDS
SMOTE 5
SMOTE 20
ADSGAN
PATEGAN
0.04
synth
0.04
synth
0.04
synth
synth
synth
real
deneity
real
density
real
denstt
0.02
real
density
0.30
real
0.02
0.02
0.02
0.00
0,00
0.00
0.00
0.00
0
200
600
0.
200
600
200
600
0
200
600
200
600
V14
V14
V14
V14
V14
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
2.0
synth
2.0
synth
2.0
synth
30
synth
synth
real
derety
real
dersity
real
deneity
2.0
real
dersity
15
real
1.0
1.0
1.0
0.0
0.0
0.0
0
20
40
60
20
40
60
0
20
40
60
20
40
60
0
20
40
60
V15
V15
V15
V15
V15
Figure 47. Subset of marginal distributions for the Bank marketing (BM) dataset. (Experiment set 2)
53

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
0.30
SMOTE
0.30
SMOTE 20
ADSGAN
PATEGAN
0.30
0.20
synth real
synth real
synth real
synth real
synth
dencity
density
0.15
density
dencily
real
0.10
0.15
0.10
0.00
0,00
0.00
0.00
0.00
10
15
10
15
10
5
15
10
Medinc
Medinc
Medlnc
Medinc
Medinc
TabSDS
SMOTE
SMOTE 20
ADSGAN
0.04
PATEGAN
0.030
0.04
synth
synth
synth
synth real
synth
0.155
real
dereity
0.020
real
dersity
0.020
real
densty
0,02
dersity
0.02
real
0.000
0.000
0.00
0.00
20
40
0
40
20
40
20
HouseAge
HouseAge
HouseAge
HouseAge
HouseAge
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.30
synth
0.4
synth
0.4
synth
synth
0.8
synth
0.15
real
dereity
real
dersity
0.2
real
densty
0.2
real
dersity
real
0.00
0.0
0.0
0.0
0
40
80
120
80
120
0
40
B0
120
0
80
120
40
80
120
AveR boms
ooms
AveR
ooms
AveRooms
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
12
12
synth
synth
synth
20
synth
synth
60
real
dereity
real
dersity
8
real
density
real
dersity
8
real
10
0
5
15
25
35
5
15
25
35
15
25
35
0
5
15
25
35
15
25
35
AveBedrms
AveBedrms
AveBedrms
AveBedrms
AveBedrms
Ta
SMOTE
SMOTE 20
ADSGAN
0.065
PATEGAN
synth
synth
synth
synth
synth
density
4c-04
real
dereity
44-04
real
dersity
dc 4c-044
real
denstty
6e-04
real
dersity
real
0c+00
0e+00
0c+00
0e400
0,000
0
10000
30000
10000
30000
0
10000
30000
10000
30000
10000
30000
Population
Population
Population
Population
Population
2.0
Ta
SMOTE
2.0
SMOTE 20
3.0
ADSGAN
2.0
PATEGAN
synth
2.0
synth
synth
synth
synth
real
deneity
real
dersity
real
denstty
2.0
real
dersity
real
1.0
1.0
1.0
10
0.0
0.0
0.0
0.0
0
200
400
600
200
400
600
0
200
400
600
200
400
600
200
400
600
AveOccup
Aveoccup
Ave0
AveŌccup
Aveō
TabSDS
SMOTE
SMOTE 20
0.5
ADSGAN
PATEGAN
0.4
synth
synth
0.4
synth
synth
0.6
synth
real
deneity
real
dersity
real
denetty
0.4
real
dersity
real
0.2
0.2
0.2
0.3
00
0.0
0.0
0.0
32
36
40
32
36
40
32
36
40
32
36
40
32
36
40
Latitude
Lattude
Latitude
Latiude
Latitude
Figure 48. Subset of marginal distributions for the California housing (CH) dataset. (Experiment set 2)
54

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabsDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth real
synth real
4
synth real
synth real
synth real
denotty
density
density
1 2 3
deriaity
2
10000
20000
10000
20000
10000
20000
10000
20000
10000
20000
eeveliingulliizatonn
TabSDS
0.030
SMOTE
0.015 0.030
SMOTE 20
0.04
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
0.015
real
dersity
0.015
real
density
real
densty
0.02
real
dersity
0.02
real
0.000
0.000
0.00
0.00
20
40
60
80
40
60
20
60
80
20
40
80
20
60
age
age
age
age
age
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
1.0
real
dereity
real
dersity
1.0
real
densty
1.0
real
dersity
real
2
0.0
0.0
0.0
0 20
100
20
60
100
0
20
1000
60
100
0
20
60 PATEGAN
100
mber0
ayy
Ta
SMOTE
SMOTE 20
ADSGAN
synth
synth real
synth
synth
synth real
10
real
dereity
dersity
8
real
density
6
real
dersity
4
2
0
10000
20000
10000
20000
0
10000 20000
10000
20000
10000 20000
atioR
DebtRatio
DeioRatio
DebiR
DebtRati
Ta
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.00010
synth
0.00030
synth
0,00010
synth
0.00015
synth
00.00010
synth
real
dereity
real
dersity
real
density
real
dersity
real
0.00000
0,00000
0,00000
0. 0.00000
0,00000
0c+00
6e+04
0e+00
6e+04
De+00
6e+004
0c+00
6c+04
De+00
6e+04
Monthlyincome
Monthlylncoome
Monthlyincome
Monthlylncome
Monthlyincome
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.08
0.12
0.08
synth
0.08
synth
0.08
synth
synth
synth
density
real
deneity
real
dersity
real
denstt
real
dersity
real
0.04
0.04
0.04
0.06
0.00
0.00
0.00
0.00
0.00
0
10
30
50
0
10
30
50
10
30
50
0
10
30
50
10
30
50
NumberoffpenCrrediiineeess
Numteroff@penCreiiiiineee...
pumberoffpemnrredtt.. pwwperrrrtttteneennnnllli
inesAndi Wumberoff0ennCrrdiiieeeeeee
Number0
www.eeeeeeeeeeeeienneeeiieee ndl
Ta
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.30
synth
synth
3.0
synth
80
synth
6.6
synth
real
deretty
real
dersity
real
density
real
dersity
0.4
real
0.15
1.5
40
0.2
0.00
0.0
0.0
0
20
60
100
0
20
60
100
20
60
100
0
20
60
100
20
60
100
NumberOfT iimbbroyy
NumberOffimes$$0Dyyttt
NumberOfT Dlyaaa
NumberOfT Lyss0yyl
Numberoffimess00ayyyat
Figure 49, Subset of marginal distributions for the Credit (CR) dataset. (Experiment set 2)
55

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.20
0.20
0.20
0.30
0.30
synth real
synth real
synth real
synth real
synth
denctty
density
density
density
real
0.10
0.30
0.10
0.15
0.00
0,00
0.00
0.00
10
15
10
15
10
10
15
15
time_ in_ hospital
time in hospital
time
haspital
time in hospital
time in hospital
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
synth real
0.015
real
derrity
0.015
real
dersity
0.015
real
densty
0.02
real
dersity
0.015
0,000
0.000
0.00
0.000
0
40
120
40
80
120
120
0
40
8D
120
40
80
120
lab procedures
lab procedures
lab procedures
lab procedures
lab procedures
0.06
TabSDS
0.06
SMOTE
0.06
SMOTE 20
ADSGAN
0.06
PATEGAN
synth
synth
synth
synth
synth
0.03
real
dereity
0.03
real
dersity
0.03
real
density
0.04
real
dersity
0.03
real
0.00
0.00
0.00
0.00
0.00
20
40
60
80
0
20
40
60
80
40
60
80
20
40
60
80
0
20
40
60
B0
num, medications
num, medications
num, medications
medications
medications
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
200
synth
2.0
synth
2.0
synth
2500
synth
3.0
synth real
real
dereity
real
dersity
real
density
real
dersity
2.0
1.0
1.0
1000
1.0
0.0
0.0
0.0
10
20
30
40
0
10
20
30
40
0
10
20
30
40
10
20
30
40
0
10
20
30
40
number_ outpatient
number_ outpatient
number outpatient
number outpatient
number outpatient
3.0
Ta
3.0
SMOTE 5
SMOTE 20
5000
ADSGAN
PATEGAN
synth
synth
synth
synth
synth real
2.0
real
dereity
real
dersity
2.0
real
denstt
real
dersity
500
1.0
1.0
2000
200
0.0
0.0
0
20
40
60
20
40
60
0
20
40
60
20
40
60
0
20
40
60
number_ emergency
number emergency
number emergency
number_ number__mergent
emergency
number_ emergency
TabS DS
SMOTE 5
SMOTE 20
ADSGAN
PATEGAN
3.0
synth
3.0
synth
3.0
synth
3.0
synth
3.0
synth real
2.0
real
deneitt
real
density
2.0
real
densty
20
real
dersity
2.0
1.5
1.0
10
10
0.0
0.0
0.0
0.0
10
15
0
5
10
15
0
10
15
5
10
15
0
5
10
15
number_ inpatient
number inpatient
number_ inpatient
number_ inpatient
number inpatient
TabSDS
SMOTE 5
SMOTE 20
ADSGAN
PATEGAN
0.8
synth
synth
0.8
synth
0.8
synth
synth
real
deretty
real
dersity
real
density
real
dersity
real
0.4
0.4
0.4
0.4
MWW
MWW
MW
0.0
0.0
0.0
0.0
5
10
15
0
10
15
5
10
15
0
5
10
15
0
10
15
number_ diagnoses
number_diagnose
number_ gnoses
number_ number_diagnoser diagnoses
number_ diagnoses
number_ diagnoses
Figure 50. Subset of marginal distributions for the Diabetes 130US (DI) dataset. (Experiment set
56

---

TabSDS: Lightweight, Fully Non- Parametriiiiic and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
3.0
anth EBI
denoty 3.0
mth
3.0
NU
snth
3.0
MU
nth al
3.0
2.0
al
density
density
2.0
densiby
2.0
al
1.5
1.0
1.0
00
0.0
00
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.8
0.0
0.4
0.0
0.4
0.8
date
date
date
date
date
TabSDS
SMOTE
SMOTE 20
1.5
ADSGAN
1.2
PATEGAN
0.8
Syyth
rea
dersity
rea
th
dersity
0.8
rea
densiyy
10
synth
ral
dersity
0.8
4nth
0.4
0.4
0.5
0.4
0.0
0.0
0.0
0.0
0.4
0.0
0.4
0.8
0.0
0.8
0.0
0.4
0.8
0.0
0.4
0.8
period
period
period
period
period
20
TabSDS
20
SMOTE
20
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
20
synth
real
dereity
real
dersity
real
densty
real
dersity
real
10
10
10
10
5
5
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
nswprice
nswprice
nswprice
nswprice
nssprric
3.0
Ta
3.0
SMOTE
3.0
SMOTE 20
3.0
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
2.0
real
dereity
real
dersity
2.0
real
density
20
real
dersity
real
1.0
1.0
1.0
1.0
1.0
0.0
0.0
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
nswdemand
nswdemand
nswdemand
nswdemand
nswdemand
2000
Ta
SMOTE
2000
SMOTE 20
2000
ADSGAN
2000
PATEGAN
2000
synth
synth
synth
synth
synth
1000
real
dereity
1000
real
dersity
1000
real
density
1000
real
dersity
1000
real
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
vicprice
vicprice
vicprice
vicprice
vicprice
TabSDS DS
SMOTE 5
SMOTE 20
30
ADSGAN
PATEGAN
synth
synth
15
synth
synth
synth
10
real
denetty
real
density
10
real
denstty
20
real
dersity
10
real
5
5
10
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
vicdemand
vicdemand
vicdemand
vicdemand
vicdemand
Ta
SMOTE
SMOTE 20
ADSGAN
PATE
synth real
synth
synth real
12
synth
synth
8
deretty
real
dersity
denetty
real
dersity
6
real
2
0.0
0.4 transfer
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4 transfer
0.8
transfer
transfer
transfer
Figure 51. Subset of marginal distributions for the Electricity (EL) dataset. (Experiment set 2)
57

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
Synth
Onth
Snnth real
0.00008
mtth al
0,00020
sy
density
6e-05
real
denotty
6e-05
real
density
6c-05
density
density
rea
0e-00
De+00
0c-00
0.00000
0.00000
-2000
4000
10000
-2000
4000
10000
-2000
4000
10000
-2000
4000
10000
-2000
4000
10000
lineNo
lineNo
lineNo
lineNo
lineNo
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
nth
nth
nnth
wnth
syfeh
0.0020
Teal
dereity
0.0020
real
dersity
0.0020
real
denstyy
0,003
al
dersity
0.004
rea
0,0000
0.0000
0,0000
0.000
0.000
100
300
100
300
100
300
100
300
100
300
as$gNo
essgNo
assgNo
a5sgNo
assgNo
0.006
TabSDS
SMOTE
0.008
SMOTE 20
0.008
ADSGAN
0.006
PATEGAN
synth
synth
synth
synth
synth
0.003
real
dereity
0.004
real
dersity
0.004
real
densty
0.004
real
dersity
0.003
real
0,000
0,000
0,000
0.000
400
B00
400
800
400
B00
400
800
400
800
prevFixD0
ur
provF ixDur
prevFixDur
prevf ixDur
prevF ixDur
TabSDS
SMOTE
0.008
SMOTE 20
0.008
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
0.004
real
dereity
0.004
real
dersity
0.004
real
densiyy
0.004
real
dersity
0.004
real
0.000
0,000
0,000
0.000
0.000
200
600
0
200
600
0
200
600
200
600
0
200
600
firstfiDDur ur
firstfiDDur
firstixDur
firstfiDDr
firstriXDur
TabS DS
0.006
SMOTE
0.006
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
0.003
real
dereity
0.003
real
dereity
0.003
real
denstty
0. 0.004
real
dersity
real
0.000
0,000
0,000
0.000
0,000
400
800
1200
0
400
800
1200
400
800
1200
400
B00
1200
0
400
800
120
firstPassFF
FxDur
asst ixDur
fisstaasFiixl
FixtDur
firstP assF ixDur
DS
0.008
SMOTE 5
0,008
SMOTE 20
0.008
ADSGAN
PATE
synth
synth
synth
synth
synth real
density
0.004
real
denetty
0.004
real
density
0.004
real
denstty
0.004
real
dersity
0.006
0.000
0.000
0,000
0.000
400
800
1200
0
400
800
1200
400
800
1200
0
400
B00
1200
400
800
1200
nextF ixDur
nextF ixDur
nextF ixDur
nEXtF ixDur
nextf ixDur
0.004
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
0.002
real
deretty
0.003
real
dersity
0.003
real
density
0.003
real
dersity
0.025
real
0,000
0.000
0.000
0.000
0.000
0
500
1500
500
1500
0
500
1500
0
500
1500
500
1500
accLen
fisttaacLenn
first5 accLen
accLenn
firstS accLen
Figure 52. Subset of marginal distributions for the Eye movements (EM) dataset. (Experiment set 2)
58

---

TabSDS: Lightweight, Fully Non- Con-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth real
synth real
synth real
synth real
synth
densityy
0.00015
dencity
0.00015
densiby
0.00011
density
0.000115
derssity
30-04
real
0.00000
0,00000
0.00000
0,00000
0e-00
0e+00
4e+06
0e+00
4e+06
0e+00
4e+06
0e+00
4e+06
De+00
4e+06
P1
P1
P1
P1
P1
TabSDS
SMOTE
SMOTE 20
20
ADSGAN
PATEGAN
20
19
synth
synth
synth
synth
synth
10
real
dereity
real
dersity
10
real
densiy
10
real
dersity
real
5
5
55
0.2
0.4
0.8
0.2
0.4
0.6
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
P5p1
P5p1
P5p1
P5p1
P5p1
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
60
synth real
dereity
synth
real
dersity
40
real
synth
densty
40
synth
real
dersity
40
synth
real
R
20
-2
20
0.0
0.4
0.B
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
P6p2
P6p2
P6p2
P6p2
P
TabS DS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
10
synth
synth
synth real
synth
synth
densivy
real
dereity
real
dersity
4
density
real
dersity
real
0.0
0.4
0.B
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
P P11p4
P11p4
P11p4
P11p4
P11p4
TabS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth real
synth
synth
real
deneity
real
dersity
6
densty
6
real
dereity
real
17
+
2
2
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.2
0.4
P14p9
P14p9
P14p9
P14p9
P14p9
TabSDS
SMOTE
SMOTE
20
ADSGAN
PATEGAN
Atth
sant
sonth
real
dereiity
dersity
mal
denstt
6
dersitty
2 4
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
0.2
0.6
1.0
P15p1
P15p1
P15p1
P15p1
P15p1
TabSDS
SMOTE
SMOTE 20
ADSGAN
120
PATEGAN
synth real
synth
synth
synth
synth
deretty
real
dersity
real
density
80
real
dersity
90
real
40
10
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
P15p3
P15p3
P15p3
P15p3
P15p3
Figure 53, Subset of marginal distributions for the House 16H (HO) dataset. (Experiment set 2)
59

---

TabSDS: Lightweight, Fully Non-Parameee Paraaetrii,,c and Model Free Approach for Generating Synthetic Tabular Data
0.020
TabSDS
SMOTE
SMOTE 20
ADSGAN
0.020
PATEGAN
synth real
synth real
synth real
synth real
synth
0.010
denotty.
0,015
density
0.015
density
0.015
densiiy
0.010
real
0.000
0.000
0.000
0
100
200
300
100
200
300
100
200
300
100
200
300
100
200
300
(Length.
fLength.
fLength.
fLength.
fLength.
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.06
0.06
synth
synth
synth
synth
synth
0.03
real
dersity
0.03
real
dersity
0.03
real
densty
0.04
real
dersiby
0.03
real
0.00
0,00
0.00
0.00
50
150
250
0
250
50
150
250
150
250
50
150
250
!Width.
IW idithh
tWidth.
[Width.
IW ldth.
TabSDS
SMOTE
SMOTE 20
1.5
ADSGAN
PATE GATEGAN
0.8
real
synth
dereity
0.8
synth
real
dersity
0.8
real
synth
densty
10
synth
real
dersity
synth
real
0.4
0.4
0.5
0.4
0.0
0.0
0.0
2
5
3
2
2
5
ize..
15ize.
iSize.
fSize.
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
2.0
2.0
2.0
synth
synth
synth
synth real
synth
real
derecit
real
dersity
real
density
2.0
dersity
real
1.
1.0
1.0
0.0
0.0
0.0
0.0
0.4
0.8
0.0
0.4
0.8
0.0
0.4
0.8
0.0
D.4
0.8
0.0
0.4
0.8
fConc.
[Conc.
[Conc.
fConc.
[Conc.
DS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
3.0
synth real
3.0
synth real
synth
synth real
3,0
synth
deneity
dersity
real
densty
1 2 3
dersity
real
2
1.
1.5
1.5
0.0
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
fConc1.
[Concl.
fConcl.
(Concl.
fConcl.
0.012
TabSDS
0.012
SMOTE
0.012
SMOTE 20
0,020
ADSGAN
0.012
PATE GAN
synth
synth
synth
synth
synth
0.006
real
dereity
0.006
real
density
0.006
real
denstt
0.010
real
dersity
0.006
real
0,000
0.000
0.000
0.000
0.000
-400
0
200
-400
200
-400
0
200
-400
200
-400
0
200
fAsym.
FAsym.
fAsym.
fAsym.
fAsym.
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
0.010
real
deretty
real
dersity
0.010
real
density
0.015
real
dersity
0.010
real
0.000
0.000
0.000
0.000
0,000
-300
-100
100
-300
-100
100
-300
-100
100
-300
-100
100
-300
-100
100
RM RM3Long.
fM BMong.
FM3Long.
IM 3Long.
3Long.
Figure 54, Subset of marginal distributions for the Magic telescope (MT) dataset. (Experiment set 2)
60

---

TabSDS: Lightweight, Fully Non- Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
0.020
TabSDS
0.020
SMOTE
0.020
SMOTE 20
0.020
ADSGAN
PATEGAN
synth real
synth real
synth real
synth real
synth
0.010
dencity
0.010
density
0.010
denstty
0.010
densiby
0.10
real
0.000
0.000
0.000
0.00
1
50
100
200
50
100
200
100
200
50
100
200
100
200
15
15
15
0.06
TabSDS
0.06
SMOTE
0.06
SMOTE 20
0.08
ADSGAN
PATEGAN
synth
synth
synth
synth
synth
0.03
real
dersity
real
density
0.03
real
densty
0.04
real
dersity
0.03
real
0.00
0,00
0.00
0.00
0.00
80
120
160
200
80
120
160
200
120
160
200
80
120
160
200
80
120
160
200
16
16
16
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.6
synth
06
synth
0.6
synth
0.6
synth
synth
0.4
real
dereity
real
dersity
0.4
real
densty
0.4
real
dersity
0.2 0.4
real
0.2
0.2
0.2
0.0
0.0
0.0
80
120
160
80
120
160
80
120
160
80
120
160
120
160
f7
17
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
1.5
synth
1.5
synth
1.5
synth
1.5
synth
2.0
synth
1.0
real
dereity
1.0
real
dersity
1.0
real
densiyy
1.0
real
dersity
real
1.0
05
0.5
0.5
0.0
0.0
0.0
80
120
160
200
80
120
160
200
80
120
160
200
80
120
160
200
80
120
160
200
f8
18
0.30
Ta
0.30
SMOTE
0.30
SMOTE 20
30
ADSGAN
PATEGAN
synth
synth
synth
synth real
synth
0.15
real
dereity
0.15
real
dersity
0.15
real
density
20
dersity
3
real
10
7
0.00
0,00
0.00
100
140
100
140
100
140
100
140
100
140
19
19
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATE
0.8
synth
0.8
synth
0.8
synth
0.8
synth
synth
real
deneity
real
dersity
real
denstty
real
density
real
0.4
0.4
0,4
1.0
0.0
0.0
0.0
0.0
0
40
80
40
80
0
40
80
40
80
0
40
80
f13
f13
f13
f13
TabSDS
SMOTE
SMOTE 20
ADSGAN
PATEGAN
0.08
synth
synth
synth
0.08
synth real
15
synth
real
denety
0.06
real
dersity
0.06
real
density
dersity
real
0.04
0.04
0.00
0.00
0.00
0.00
0
40
80
120
40
80
120
0
40
80
120
40
80
120
0
40
80
120
f14
f14
f14
fL4
Figure 55. Subset of marginal distributions for the Pol (PO) dataset. (Experiment set 2)
61

---

TabSDS: Lightweight, Fully Non- Parammaametrc, and Model Free Approach for Generating Synthetic Tabular Data
TabSDS
(D)
ddpm
arf
42
Synth
synth real
synth
40
40
38
Lattude
Latttzk
L
35
30
34
m
-124
-120
-116
-124
-120
-116
-124
-120
-116
Longitude
Longitide
Longhtude
(d)
tvae
(e)
ctgan
bayesnet
42
52
synth
synth
synth
real
40
40
La 20mud
393
Latuue
Latbadk
30
36
36
-120
-116
-124
-120
-116
-124
-120
-116
Longitude
Longitude
Longitude
Figure 56. Scatter plots of Latitude versus Longitude in the California housing (CH) dataset.
G.9. Evaluation of the Influence of the Sampling Proportion Parameter
All the TabSIDS results presented in the main text were computed using p 0.5. Here, report and compare results based the nosier choice of 0.1. Figures 57 to 68 report the detection test, ML efficiency, domias MIA, and DCR distributions over on the same grid of 24 ne values before. Results based p 0.1 and 0.5 are shown in blue and red, respectively. Overall, the adoption of noisier marginal distributions (lower p) lead to an accentuated degradation of the detection test (note the considerably higher detection scores in panel a across most figures) without a corresponding improvement in privacy. (Overall, we do not see very accentuated differences panels e and d across the figures.) For this reason, we adopted p 0.5 in our evaluations.
detection test
(b) ML efficiency
Domlas MIA
d
DCR distributions
0.35
0.25
0.5
=01 0.1
0.20
p 0.1
0.58
metric
metric
0.45
Frstre
0.15
0.80
0.10-
-8080
0.35
p
0.5
0.54
0.5
0.05
001
0=1.1
0.00
200
1000
200
600
1000
200
600
1000
27
37
00
20
80
80
100
300-
400-
500
600
700
900
1000-
nc
n;
ne
Figure 57. Abalone (AB).
detection test
(b) ML efficiency
(C)
Domias MIA
0.9
p 0.5
0.80 0,890
0,80
O
0
0.1
mebric
0.7
metric
metric
0.76
0.700
0.6
=
0.5
0.5
00
0
0
0
0,860
p =
0.1
0.72
0=1.1
0
200
600
1000
200
600
1000
200
600
1000
Figure 58.
Adult (AD).
62

---

TabSDS: Lightweight, Fully Non- Pon-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
detection test
(b) ML efficiency
(C)
Domias MIA
100 (d)
DCR distributions
0.395
p=0.5
0.85
00000000000
0.5
0.85
p=0.1
0.385
80
9
mebii
metric
0.75
0.373
88
40
0.65
p 0.1
0.5
355
0.1
20
0
200
600
1000
200
600
1000
200
600
1000
20
30
35
40
50
60
70
80
90
200-
300
400
500-
600
700
900
1000-
Figure 59. Bank marketing (BM).
detection test
(b) ML efficiency
Domias MIA
(d)
DCR distributions
0.30
0.5
8
0.1
0,52
#01
0.70
metric
0.80
metric
DCR
0.48
0.60
0.50
=
0.5
0.44
0.5
p
0.1
200
1000
200
600
1000
200
600
1000
10
35
300
400
500
600
700
800-
900
1000
Dg
De
Figure 60. California housing (CH).
detection test
(b) ML efficiency
0.38
Domias MIA
(d)
DCR distributions
0.80
15-
0.1
metii
metric
metric
0.36
DCR
10-
0.70
p
0,50
0=1.1
0.34
0.1
200
1000
200
600
1000
200
600
1000
10
20-
25
30
35
40
50-
60
70
80
90
100
300-
400
500
600
700
900
1000-
ng
De
Figure 61. Credit (CR).
detection test
(b) ML efficiency
Domias MIA
(d)
DCR distributions
0.5
0.02
00808088
0.52
0=5
0.1
p 0.1
metric
metric
0.58
metric
0,50
1.5
0.65
1.0
p
0.5
0.54
p
0011
0.48
0.1
0.0-
200
600
1000
200
600
1000
200
600
1000
100
300-
100
500
600
700
900
1000-
nc
ne
Figure 62. Diabetes 130US (DI).
a) detection test
(b) ML efficiency
(C) Domlas MIA
(
DCR distributions
0.12
0.5
0.90
0.5
0.95
p 0.1
0.10
p =01
0.52
0.08
netric
0.90
metric
0.80
metric
0.06
0.04
p
50
0.5
0.02-
0.70
p
=
0.1
0.1
0.00-
0
200
600
1000
200
600
1000
200
600
1000
30
80
60
70
20
90
300
1000
500-1
600
700
900
1000
Figure 63. Electricity (EL).
63

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
(a)
detection test
(b) ML efficiency
(C) domias MIA
(d)
DCR distributions
0
500
==0.1
0.02
=01
0.90
400-
metiic
metric
metric
300
0.58
200
P =
100
0.54
0.1
600
1000
20-
25
80
35
40
50
60
70
80
90
100
200
300
400
500-
600-
700
900
1000-
fgc
ng
Figure Eye movements (EM),
detection test
(b)
ML efficiency
(c) domias MIA
DCR distributions
0.5
0.94
0000000
0-5
0.95
p.1
#01
0.50
metric
metii
OCR
9
0.98
2-
0.82
P - 0.1
200
600
1000
200
600
1000
20
72
20
50
80
70
30
100
300
400
500
600
700
900
1000
nce
Figure 65. House 16H (HO).
detection test
(b) ML efficiency
Domias MIA
d
DCR distributions
p 0.5
0.92
00000000
0.41
50-
p 0.5
0.1
p 0.111
40
0.8
metric
metric
0.88
metricc
0.39
30
0.7
20
066
=
= 0.5
10
0.5
8
8
8
0.84
p
0.37
0.1
200
600
1000
200
600
1000
200
600
1000
10-
15
35
80
60
70
80
90
200-
300
400
500
600
700
900
1000-
ng
Figure 66. Magic telescope (MT).
detection test
(b) ML efficiency
Domias MIA
0 0:0000000000000
0,66
0000000
0.5
0.1
0,9995
0.3
0,52
meti
metric
meltiic
077
0.58
0.9985
0.6
p 0=0.5
0.5
0.1
0.54
0.1
600
1000
200
1000
nc
ng
ng
Figure 67. Mushroom (MU). (Note that for purely categorical datasets the choice of p is immaterial since is not used in the Categorical- SJPPDS algorithm (Algorithm 4).)
1.00
detection test
(D) ML efficiency
Domias MIA
(d)
DCR distributions
2790
0.5
40-
p 0.5
0.1
0.990
001
30-
mevic
metri
mettt
0.780
0.980
20
0.570
p 0
0.5
p
0.770
14
200
1000
200
600
1000
200
600
1000
40
30
80
70
80
30-
100
200-
300-1
400
500-
600
700
900
1000-
nc
n:
ncc
Figure 68. Pol (PO).
64

---

TabSDS: Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data
X
(a)
Y()
X
Z(
10
12
(()
(b)
(())
(
Z()
-2
8
10
12
qaplot
(c)
(d)
0 oomoooo.o oo
synthetic
real
Frequency
synthetic
-2
8
10
8
12
variable data
real
Figure 69. Problematic case for Algorithm 3: multimodal distributions with discontinuous support. To illustrate this problematic case, consider variable with bimodal distribution with modes centered at and 10 and with discontinuous support between the modes. The real data is shown in the (m) = (X()): X(2)..... X(30)) rows in panels a and h, and the blue histogram in panel c. (Note that there values in the mode round 10. Panels a and b show the synthetic data (red points) generated, respectively, by two calls to Algorithm 3. (0) (Y(), Y. Y(15)) and (s)) (Z(), Z(z)..., ((1))) represent the sorted subsamples of m 15 (randomly drawn from X). The dotted lines connect the elements of same order in Y (s) and Z(g (i.e., Y(1) is connected to Z(1)- Y(2) to Z(2), and so on). Algorithm may generate synthetic values outside training data range (grey bands) whenever the number points in Y (i) and
real data values (blue dots) between and this example, n 30, with 15 values in the mode around 0 and 15
Z ()) within given mode are different. For instance, in panel the mode around 0 contain 8 points (Y()). Y(2).... ........Yy Y(s)) belonging to
(6), and points (7)),, 7(2)- Z(m) belonging to (()) whereas mode around 10 contain points (Vo), Y(10)- Y(15) in Y and points (7(z); 7 7(5) in Za) As consequence, we have that Y(s) belongs to the 0 mode while Z(s) belongs to the
10 mode, and the algorithm ends generating synthetic value X(s) 4.63 outside the range of X. A similar issue happens in panel b because mode contains points in Y (1) and points in (z) and mode contains points ()) and points (o) This issue can, nonetheless, be casily resolved by generating additional synthetic samples and discarding samples outside the range of the training data.
65


Reviews:
[{"review_id": "2Tbxvodjgh", "reviewer": "Reviewer_9VCx", "summary": "The paper introduces TabSDS, a non-parametric, lightweight framework for generating synthetic tabular data. The approach is based on the Sequential Joint Probability Preserving Data Shuffling (SJPPDS) algorithm, a perturbation method that relies on restricted feature permutations to preserve the joint distribution of the data. Specifically, given T columns or features, the algorithm performs multiple restricted permutations of T-1 columns with respect to the remaining column. Each column's data is shuffled, ensuring that the marginal distributions are preserved.  \n\nThe authors extend this approach by generating new data for each feature, effectively providing synthetic data while enhancing privacy. This generation process is carried out using a new algorithm called IOSSampler, which samples new data uniformly from the values of ordered sub-samples of the input feature.  \n\nThe proposed method is significantly faster than existing deep learning and machine learning approaches, while it trades off privacy for better realism.\n\n## update after rebuttal\nThe authors addressed some of my concerns, but I believe the generation of new data --- in practical settings --- could be improved. I keep the original score.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for the very thoughtful comments and questions. \n\n>Q1. In Tables 2 and 3, does the method requires for the same category to have different ranking?\n\nYes, it requires different ranks for each category. The problem is that if you assign the same rank value for each category the restricted permutation generates an identical copy of the real data (except for the order of the rows). The linked table https://drive.google.com/file/d/12OXRKwkT06lokekRKe42VOjANX0RJytV/view?usp=sharing shows an illustrative toy example, where the original categorical data is recoded as $X_1=[C \\equiv 1, D \\equiv 2]$ and $X_2=[A \\equiv 1, B \\equiv 2]$, and perm. 1 to 4 represent restricted permutations of $X_1$ relative to $X_2$ (where we shuffle the values of $X_1$ within each level of $X_2$). Clearly, this approach cannot be used for datasets containing only categorical variables. Having different ranks for the same category is necessary for generating distinct datasets, while still preserving the joint distribution to a good extent. (Also, it helps unify the treatment of categorical and numeric variables in mixed datasets.)\n\n>Q2. In algorithm 3 will the input and real distributions match for bimodal distributions? How to choose the value for m?\n\nYes, the synthetic and real distributions will match if the bimodal distribution has continuous support (e.g., bottom left panel of Fig. 29). However, for a discontinuous bimodal distribution—where values cluster near 0 and 10 with no training examples in between—the method may generate a small fraction of intermediate values outside the training range. Thanks for noting this edge case; we will mention it in the Limitations section and indicate that some post processing might be necessary in this case.\n\nFor the choice of m, note that m = floor(n * p), where n is the number of samples and 1/n <= p <= 0.5.  Hence, m can vary from 1 to floor(n/2). As described in page 6 (lines 292 to 300 in the 2nd column) we found that lower values of p can lead to considerable decreases in data fidelity without comparable increases in privacy. Hence, in practice, we recommend taking m = floor(n/2).\n\n>Q3. models were tested on a CPU instance. Given the computational demands of deep models like TabDDPM, how many training epochs were used?\n\nThe number of training epochs was one of the parameters evaluated during hyperparameter optimization (or taken from other works) using the hyperpar. search spaces defined in Synthcity. We will add tables of hyperpar. values to the final version of the paper. For TabDDPM, the number of epochs ranged from 1051 to 8300, and the experiments run for long times on the CPU instance.\n\n>benchmarks could include SMOTE and CTABGAN+\n\nWe restricted our comparisons to models available in Synthcity. Since Kotelnikov et al (2023) performed extensive comparisons of these weaker baselines against TabDDPM, and we performed comparisons against TabDDPM, we feel these additional comparisons might not be essential. But, please, let us know if you disagree (as we might be able to implement SMOTE and report results over the discussion period).\n\n>In Table 4 the # of features appears to differ from the cited paper\n\nTable 4 reports # of variables (i.e., # of features plus the target) while the Table 4 in Hansen et al 2023 reports only # of features. (Also, for the California housing we used the sklearn data rather than Hansen’s.) We will clarify these points and add specific URL/references for each dataset in the appendix.\n\n>novelty of the proposed approach should be better explained\n\nCompared to Chaibub Neto (2024), we extend SJPPDS to categorical data while also generating synthetic marginal distributions. This improves practicality: first, handling categorical variables makes our approach more widely applicable (as tabular data is often mixed). Second, even for purely numeric data, our method offers better protection against trivial membership inference attacks (which SJPPDS cannot prevent) when datasets contain unusual attribute values which can be easily spotted by an attacker.\n\nOur approach differs from Domingo-Ferrer et al (2025) in 3 key ways. First, we generate marginals via order statistics interpolation, whereas they require the user to choose predefined parametric distributions (e.g., Gaussian, Gamma). Second, we extend SJPPDS to categorical variables, while they employ a more complex ontology-based semantic ranking [1] (what is also more involved in practice). Third, we use SJPPDS for rank data shuffling, whereas they rely on different algorithms.\n\n[1] Domingo-Ferrer et al (2013). Information Sciences 242:35-48.\n\n>In large datasets, category granularity can be an issue. How to select the correct hyper-parameters?\n\nFor deep learning and ML baselines, we optimized hyperparameters using Optuna within Synthcity's defined search spaces or adopted values from Hansen et al (2023), which were also optimized with Optuna in Synthcity.\n\nPlease, let us know if you have any further questions.", "claims_and_evidence": "Yes, claims are supported by theorems/proofs and experiments.", "methods_and_evaluation_criteria": "The proposed method and evaluation is reasonable. The selected benchmarks could be extended, including for example a shallow interpolation-based methods, e.g., SMOTE (Chawla et al., 2002).", "theoretical_claims": "Theorem 4.1 seems correct to me, but I didn't check the formal proof.", "experimental_designs_or_analyses": "The datasets are not explicitly linked, and in Table 4 the number of features (num and cat) appears to differ from the cited paper where these datasets were originally used, as well as from other related studies (TabDDPM). To improve reproducibility, I suggest adding the specific URL or reference for each dataset, at least in the appendix.  \n\nAdditionally, the authors mention that all models were tested on CPU instance (with 8 cores). Given the computational demands of deep learning models like TabDDPM, I would like to ask about the number of training epochs used. If the models were not trained sufficiently, it could explain potential performance limitations.", "relation_to_broader_scientific_literature": "The paper addresses an important topic: synthetic tabular data generation. While it differs from existing deep learning and machine learning models, it builds and extends an interesting line of research, particularly relevant are the work of Chaibub Neto, 2024 (SJPPDS), and the work of Domingo-Ferrer et al. (2025).", "essential_references_not_discussed": "None", "other_strengths_and_weaknesses": "Strengths:\n- The paper addresses an important topic, proposing a new non-parametric lightweight method . \n- The method has very good performance in terms of utility and realism. \n- The method could be a good alternative solution to more expensive and classic DL/ ML approaches. \n\nWeaknesses: \n- The novelty of the proposed approach compared to existing work should be better explained. In particular, compared to Chaibub Neto (2024) and Domingo-Ferrer et al. (2025), the main contribution appears to be a lighter approach to fit marginal distributions and generating synthetic samples. \n- I have some concerns about the evalution. The method has very good performance in utility and realism, but privacy may be a problem. Also the real and syn marginal distributions seem really close. Some benchmarks are missing (e.g., SMOTE, CTABGAN+), while some details are missing. \n\nSee other comments and questions.", "other_comments_or_suggestions": "- Acronyms in Section 2 maybe should be capitalized, e.g., *DDPM* instead of *ddpm*.\n\n- The datasets used in the paper (table 4) seem to have a different number of columns compared to the original paper and TabDDPM.  For exampel, the columns *#num* and *#cat* list feature for numerical and categorical. But House_16H appears to have 17 features instead of the 16 features in the cited Hansen et al. (2023).\n  \n- I suggest that to improve reproducibility, consider providing a URL where the exact datasets can be downloaded. And also add details on training epochs for benchmarks\n  \n- In large datasets with many columns and values, category granularity can be an issue—some categories may be too broad or too fine-grained, leading to sparsity or excessive heterogeneity. How to handle that and select the correct hyper-parameters?\n\n- Theorem 4.1 is cited ad Theorem 1.", "questions_for_authors": "Q1: In the examples of Table 2 and Table 3, does the method requires for the same category to have different ranking? Is possible to ahve the same ranking for the category A, and what's the impact of doing that? Different ranks, could \"break\" the join distributions in the synthetic data? \n \nQ2: In algorithm 3: while the distribution is expected to converge as *m* → ∞, in practice, will the input and real distributions actually match for like bimodal distributions? How to choose the correct value for m? For example a bimodal distribution with values clustering around 0 and 10? When we sample: uniform(0, 10) we can get values not in the real/training set? \n \nQ3: The authors mention that all models were tested on a CPU instance (with 8 cores). Given the computational demands of deep learning models like TabDDPM, I would like to ask about the number of training epochs used. If the models were not trained sufficiently, it could explain potential performance limitations. How they handle this possible limitation?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3Igt5cEnHB", "reviewer": "Reviewer_Ai12", "summary": "The paper introduces TabSDS, a non-parametric and model-free method for generating synthetic tabular data. Unlike deep generative models (DGMs), which are computationally expensive and require extensive hyperparameter tuning, TabSDS leverages rank-based transformations and data shuffling to approximate the joint probability distribution of real data. The method extends sequential joint probability preserving data shuffling (SJPPDS) by incorporating categorical features and generating entirely new data points rather than merely shuffling existing data.\n\n## update after rebuttal\n\nI thank the authors for their rebuttal and remain positive about the work.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your thoughtful comments and questions.\n\n>How does TabSDS compare to differentially private synthetic data methods?\n\nWe now included comparisons with two additional DP based methods available in Synthcity: ADSGAN [1] and PATEGAN [2]. (We also evaluated the DPGAN [3] but didn’t include it in the comparisons because it was considerably slower and tended to generate considerably lower fidelity data.)\n\nDue to time constraints, we were unable to optimize the hyperparameters of these two DP-based generators, and the results presented here are based on the default hyperparameter values in Synthcity. (Hence, they should be taken with a grain of salt and are aimed for the appendix.)\n\nFollowing a suggestion by Reviewer Y1nw we now evaluate the methods wrt 2 additional privacy metrics, the sorted version of Distance Based Record Linkage (DBRL) metric, which measures robustness to re-identification attacks; and the sorted version of the Standard Deviation Interval Distance (SDID) metric, which measures robustness to attribute disclosure attacks. The standard versions of the DBRL [4] and SDID [5] metrics are traditionally used in the Statistical Disclosure Control field to evaluate perturbation methods.  Application to synthetic data requires a prior sorting step as described in [6]. (The basic idea is to sort the rows of both the original and synthetic datasets according to the values of a given column of the data prior to the computation of the DBRL and SDID metrics.)\n\nAfter the sorting step, the DBRL metric is implemented by computing the Euclidean distances between each record in the synthetic dataset against all records in the real dataset. A synthetic record is considered “linked” when the nearest record in the real data turns out to be the corresponding real record. The metric is defined as the proportion of synthetic records linked to real records. After the sorting step, the standard SDID metric corresponds to the proportion of real records inside a standard deviation interval whose center is the corresponding synthetic record.\n\nFollowing the suggestion of Reviewer r8L7, to better facilitate the visualization of the tradeoffs between privacy and fidelity we now report plots comparing these two new privacy metrics against the Energy Distance (ED) fidelity metric. (ED is closely related to maximum mean discrepancy and can be used to measure the distance between 2 multivariate distributions.)\n\nFigures 1 to 4 in the linked pdf report these comparisons: https://drive.google.com/file/d/1M93WfhXtWQVRLXsvsgoac0S1O_kAqjt_/view?usp=sharing Figure 1 shows scatterplots of ED vs DBRL for the original methods and ADSGAN. Overall, TabSDS tended to generate higher fidelity data than the other methods (the red dot tends to be closer to 0), while ADSGAN tends to generate lower fidelity data (the inverted purple triangle tends to be farther from 0 than most methods on most of the datasets). In terms of re-identification risk, all methods generated low risks (below 2.5% across all datasets) and none of the methods stood out as systematically better or worse than the other methods. Not even ADSGAN tended to do systematically better on this metric. This might, however, be due to the fact that the default hyperparameter value in Synthcity is set for moderate privacy protection (or due to suboptimal model training).\n\nFigure 2 shows analogous results for the ED vs SDID comparison. Again, the SDID risk tended to be low for all methods (and was 0 for ADSGAN across all datasets). Figures 3 and 4 add the comparisons against PATEGAN (open purple diamond). Overall, PATEGAN tended to achieve considerably lower data fidelity than ADSGAN (note the extended x-axis).\n\n[1] Yoon et al (2019) Anonymization through data synthesis using generative adversarial networks (ADS-GAN): a harmonizing advancement for AI in medicine.\n\n[2] Jordon et al (2019) PATE-GAN: generating synthetic data with differential privacy guarantees.\n\n[3] Xie et al (2018) Differentially private generative adversarial network.\n\n[4] Domingo-Ferrer and Torra (2001) A quantitative comparison of disclosure control methods for microdata.\n\n[5] Mateo-Sanz et al (2004) Outlier protection in continuous microdata masking.\n\n[6] Chaibub Neto (2024) Statistical disclosure control for numeric microdata via sequential joint probability preserving data shuffling.\n\n>How does TabSDS handle imbalanced categorical variables?\n\nWhen categorical variables are imbalanced, synthetic data generators can struggle to preserve the frequencies of rare categories observed in the real data.\n\nThis is not an issue for TabSDS which, by construction, preserves the marginal distribution of the categorical variables (since the data from each categorical variable is simply shuffled around, so that the marginal frequencies of the categories are preserved).\n\nThanks again, and please let us know if you have any further questions.", "claims_and_evidence": "Claim 1: TabSDS offers competitive fidelity and utility compared to state-of-the-art models. -- Supported by benchmarking against TabDDPM, ARF, TVAE, CTGAN, and Bayesian networks using the Synthcity library. Results demonstrate strong performance in fidelity and downstream ML utility.\n\nClaim 2: TabSDS is significantly faster than both deep generative models and adversarial random forests (ARF). -- Experimental results show orders-of-magnitude improvements in runtime across multiple datasets.\n\nClaim 3: TabSDS improves privacy compared to deep generative models. -- Measured via membership inference attack (MIA) success rates, showing reduced susceptibility compared to deep models and ARF.", "methods_and_evaluation_criteria": "The evaluation settings and criteria are appropriate to support the claims.\n\nThe evaluation assess fidelity (ROC AUC on synthetic vs. real detection), utility (ROC AUC on downstream ML tasks trained with synthetic data) and privacy (Membership inference attack (MIA) success rate). These characteristics are suitable and the metrics used appropriate.\n\nThe comparisons baselines are TabDDPM, ARF, TVAE, CTGAN, and Bayesian networks, which is a good representative set of the main synthetic data generation methods for tabular data.\n\nEvaluation includes 12 datasets containing mixed numerical and categorical data. These datasets are often used in the literature.", "theoretical_claims": "I checked the proof of Theorem 4.1 (Rank-matching step: Maintains the joint probability distribution of the original data). They look senseful to me but I cannot guarantee it.", "experimental_designs_or_analyses": "Yes. The evaluation looks sound to me (cf. metric and evaluation criteria section). Experiments were repeated 10 times to account for random factors.", "relation_to_broader_scientific_literature": "The key contribution is to propose a new tabular data generation method that is more efficient than state of the art approaches (like deep generative models) while remaining of quality in terms of fidelity, utility and privacy. Tabular data generation remains an unsolved problem (or at least, existing solutions are not entirely satisfactory) so I believe there is value in pursuing research in this area. The proposed approach rely on SJPPDS, which is novel compared to the usual practice of the literature.", "essential_references_not_discussed": "The paper could benefit from a comparison with differential privacy-based synthetic data generation methods.", "other_strengths_and_weaknesses": "Efficiency: Faster than generative models, with minimal parameter tuning required.\n\nFlexibility: Handles both categorical and numerical data, unlike SJPPDS.\n\nPrivacy-Utility Tradeoff: Provides explicit control over fidelity and privacy through the nc parameter.", "other_comments_or_suggestions": "None", "questions_for_authors": "How does TabSDS compare to differentially private synthetic data methods?\nHow does it handle imbalanced categorical variables?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "i98f4eEv1R", "reviewer": "Reviewer_Y1nw", "summary": "The paper proposes a novel method for synthetic data generation. This new method is based on two basic actions: generating new values for each of the features by sampling through from its \"interpolated marginal\", then shuffling the original data following the algorithm SJPPD and then matching the ranking of the shuffled data with the synthetic ones.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your comments and thoughtful suggestions. While we could only address your main concerns here, we would be happy to follow up on the remaining ones (or any additional questions) during the discussion period. Please, let us know.\n\n>One of the worries I have is what happens when the number of features increases. Wouldn't the distribution become more and more similar to the distribution obtained with random shuffling?\n\nNo. The sequential joint probability preserving data shuffling approach employed to shuffle the data is designed to preserve the association structure of the data columns, irrespective of the number of columns.\n\nTo illustrate this point, we:\n\n1. Simulated a dataset $X$ from a multivariate normal distribution of dimension 200 (with a highly structured correlations).  In our experiment, this simulated data plays the role of the “real” data.\n\n2. Applied TabSDS to subsets of $X$ with increasing numbers of features.\n\n3. Compared how synthetic datasets generated by TabSDS recapitulated the real data's correlation structure as the number of features increased.\n\nExplicitly, in our experiment, we considered 10 subsets of $X$, composed, respectively by the first 20, 40, …, 180, and 200 features of $X$.\n\nFor each of the 10 subsets, we generate synthetic data (using the same $n_c$ value) and computed the correlation matrices of the real and the synthetic data subsets. To measure how well the synthetic data recapitulated the correlations of the real data we computed the L2 distance (L2d) between the correlation matrices (define as average($(r_j – s_j)^2$), where $r_j$ and $s_j$ represent entries of the real and synthetic data cor. matrices and the average is taken over the upper (or lower) diagonal entries of the matrices).\n\nThe above procedure was repeated using $n_c$ values set to 5, 10, 15, 20, 25, and 30.\n\nThe results are reported in Figures 1 to 5 on the linked pdf file: https://drive.google.com/file/d/1dB9Vsb0IucFZBCft_k13Ljb82FXr0zE1/view?usp=sharing\n\nFigure 1a reports the values of the L2d for each of the 10 subsets. (Each boxplot reports the L2d values across the 6 distinct $n_c$ values.) Figure 1b shows the L2d values across the 10 subsets for each of the $n_c$ values. As expected, larger $n_c$ values lead to higher fidelity synthetic data and lower L2d values. This figure shows that the ability to recover the correlation structure of the real data remains largely constant as we increase the number of features from 20 to 200. (We would expect to see an upward trend if the method’s performance worsened with larger number of features.)\n\nFinally, Figures 2 to 5 compare the correlation matrices of the real and synthetic data for subsets of 20, 40, 100, and 200 features (based on $n_c = 30$). They illustrate how TabSDS is able to recover very well the correlation structure of the real data across all these subsets.\n\n>In the comparison some key methods are missing. In particular: WGAN and GReaT\n\nWe restricted our comparisons to generators implemented in Synthcity. While GReaT is available, preliminary checks showed it was computationally unfeasible to include it in our comparisons (we run our experiments in CPUs). (Also, recent work by Zhang et al. (2024) [1] has shown that GReaT tends to be outperformed by TabDDPM - which is included in our comparisons.) WGAN is not available in Synthcity.\n\n[1] Zhang et al (2024) Mixed-type tabular data synthesis with score-based diffusion in latent space. ICLR 2024.\n\n>the authors assessed robustness of the generated data wrt membership attacks ... it would be interesting to also evaluate robustness wrt attribute disclosure attacks and re-identification attacks\n\nThis is an good suggestion. We have now included new evaluations based on the sorted versions of the Standard Deviation Interval Distance (SDID) and Distance Based Record Linkage (DBRL) metrics (which measure robustness to attribute disclosure and re-identification attacks, respectively). Please, see our reply to Reviewer Ai12 for further details about these metrics.\n\nAs suggested by Reviewer r8L7, we now report these new results using tradeoff curves comparing these privacy metrics against the Energy Distance (ED) fidelity metric. Results are presented in the linked pdf file: https://drive.google.com/file/d/1PYa_pgyQqqWwPI0Dq0ichscMmYftoyfK/view?usp=sharing Please, see our reply to Reviewer r8L7 for the interpretation of these results.\n\n>it would be interesting to have a discussion/analysis of the relationship between n_c and the privacy metrics. If n_c grows, can we still retain good privacy values?\n\nAs $n_c$ grows, TabSDS generates less private data. This point is discussed in lines 376 to 380 of the manuscript. Also, Figure 4 (main text) and Figures 11d - 22d (Appendix) illustrate this by showing decreasing DCR privacy metric values as $n_c$ increases. Similarly, panels e and f of Figures 1-10 (see the linked pdf file) show rising disclosure risks in sorted DBRL and SDID metrics as $n_c$ grows.", "claims_and_evidence": "One of the worries I have with this paper is what happens when the number of features increases. As the number of features increases, we keep shuffling. Wouldn't this make the distribution of the features become more and more similar to the distribution obtained with random shuffling? \n\nIn your experimental analysis the authors tested the method with datasets with up to 27 features. What happens if we take datasets with 100 or more features? \n\nFinally, it would be interesting to have a discussion/analysis of the relationship between $n_c$ and the privacy metrics. If $n_c$ grows, can we still retain good privacy values?", "methods_and_evaluation_criteria": "In the methods used for comparison some key methods are missing. In particular: WGAN [Arjovsky et al., 2017] and GReaT [Borisov et al., 2023]. \n\nIn the metrics used for privacy, the authors used assessed the robustness of the generated data wrt membership attacks. \nHowever, it would be interesting to also evaluate its robustness wrt attribute disclosure attacks, (i.e., try to gain access to sensitive attributes of an entity from the real dataset) and re-identification attacks (i.e., attacks try to map a synthetic data point back to the original dataset)", "theoretical_claims": "See claims and evidence box", "experimental_designs_or_analyses": "Given that the model is not always the best performing model it would be useful to perform a Friedman statistical test (once you have included also Great and WGAN) together with a Nemenyi test to check the statistical significance of your results. For more info see (Statistical Comparisons of Classifiers over Multiple Data Sets, Demsar, 2006).", "relation_to_broader_scientific_literature": "The authors have covered good part of the literature", "essential_references_not_discussed": "All the essential references are discussed.", "other_strengths_and_weaknesses": "No other strengths and weaknesses need to be discussed.", "other_comments_or_suggestions": "The paper contains a lot of algorithms, which often are not even needed and risk to simply confuse the reader. For example, algorithm 8 is simply the application to every column of the matrix $\\mathbf{X}$ of the algorithm InterpolatedOrderStatsSampling. \n\nFigures are also not aligned well (see, e.g., Figure 5c and 5d). \n\nFinally the na,e of the other methods (e.g., TVAE) should be capitalized following the capilazion given by the authors.", "questions_for_authors": "Please see the boxes above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1W1qKa9uiA", "reviewer": "Reviewer_r8L7", "summary": "This paper introduces a model-free approach for synthetic data generation based on direct data perturbation. The method operates by sequentially shuffling feature values while conditioning on binned representations of other features. The authors compare their approach to generative models, evaluating its effectiveness in generating synthetic data.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your very thoughtful comments/suggestions. We address below your main concerns, and we would be happy to follow up on the remaining ones (or any additional questions) during the discussion period. Please, let us know.\n\n>Authors should compare to approaches based on adding noise data … My main concern is with the choice of privacy metric and how the comparisons are presented. Comparison should be made using plots which show the full tradeoff curve between privacy and utility.\n\nWe now included new comparisons with the additive noise approach using 2 new privacy metrics (and display the results using privacy/utility tradeoff curves as suggested).\n\nFollowing the suggestion of Reviewer Y1nw, the new adopted metrics are the sorted versions of the Standard Deviation Interval Distance (SDID) metric (which measures robustness to attribute disclosure attacks), and the sorted version of the Distance Based Record Linkage (DBRL) metric (which measures robustness to re-identification attacks). Please, see our reply to Reviewer Ai12 for further details about these metrics.\n\nWe also adopted Energy Distance (ED) as a fidelity metric. (ED is closely related to MMD and can be used to measure the distance between 2 multivariate distributions.)\n\nWe implemented the noise addition comparison using the sdcMicro R package. Noise addition was evaluated over a grid of 13 increasing levels of additive noise ranging from 1% to 50% of the standard deviation of each variable.\n\nFigures 1-10 in the linked pdf report the results: https://drive.google.com/file/d/1PYa_pgyQqqWwPI0Dq0ichscMmYftoyfK/view?usp=sharing\n\nIn each figure, panel a show the ED vs DBRL tradeoff curves for noise addition (blue) and TabSDS (black). The red dot represents the selected value of $n_c$ based on the DCR criterium, while the purple symbols represent the other baseline generators. To better compare the generators, panel b shows the same results without displaying the noise addition curve. Panels c and d show analogous results in terms of the ED vs SDID tradeoff. To further illustrate the influence of the amount of noise and of $n_c$ on these privacy and fidelity metrics, panels e-i show the metric values against the perturbation parameter values.\n\nInspection of the figures shows that:\n\n1. TabSDS usually achieves a better ED vs DBRL tradeoff than the additive noise approach (note how the black curves are usually closer to the bottom left corner than the blue curves in panel a).\n\n2. TabSDS tends to achieve better fidelity (lower ED) than the other approaches (the red dot tends to be closer to 0).\n\n3. In terms of re-identification risk (panel b), all methods generated low risks (below 2.5% across all datasets) and none of the methods stands out as systematically better or worse than the other methods.\n\n4. In terms of attribute disclosure (panel d), again, the risks tended to be low for all methods.\n\n>While these extensions are interesting, I still believe that the question of originality arises. The second point [extension to categorical variables] seems rather trivial and the impact of the first [generating new values for numerical features] is not analyzed regarding additional privacy.\n\nRegarding the extension to categorical variables, while our approach is simple, alternative approaches based on the computation of ranks on categorical variables are considerably more involved and difficult to implement in practice. For instance, [1] proposes the use of an ontology-based semantic distance.\n\nRegarding the evaluation of additional privacy protection achieved by new values, in our new evaluations we also compare TabSDS against a simplified version of the algorithm (denoted TabSJPPDS), which discards the new value generation step. The results are presented in panels e, f, and g of Figures 1-10 on the pdf linked above. Overall, generating new values improves privacy protection, as shown by the lower disclosure risks of TabSDS (black) relative to TabSJPPDS (brown) in panels e and f. As expected, generating new values also lead to a decrease in fidelity, as illustrated by the higher ED values of TabSDS relative to TabSJPPDS (panel g).\n\nFinally, note that these extensions have important practical impacts. First, by handling categorical variables TabSDS can be much more widely applied than SJPPDS (since tabular datasets often contain mixed data). Second, even for exclusively numeric datasets, in addition to the better re-identification and attribute disclosure protection, TabSDS also offers better protection against a trivial form of membership inference attack for which SJPPDS is helpless. (Namely, for datasets containing unusual values, an attacker might immediately infer membership by recognizing the presence of unique values of a given record in the perturbed dataset.)\n\n[1] Domingo-Ferrer et al (2013). Information Sciences 242:35-48.\n\nThanks again for your review, and let us know if you have any additional questions.", "claims_and_evidence": ">[...] it extends SJPPDS from a data perturbation approach (where the data is shuffled but no new values are generated) into a fully synthetic data method.\n\nWhile the authors introduce an initial step aimed at producing new values for numerical features that did not exists in the training set, in my view, the proposed method should still be classified as a data perturbation approach as it is not unlike adding noise to an existing dataset. \n\nThe authors compare their method with generative models which are forced to compress a dataset into a set of model parameters which are then used to generate new data. To me, this seems like a fundamentally different approach.\n\n> In addition to being easier to tune, this allows for a very precise control of the trade-off between data utility/fidelity and data privacy\n\n[**Resolved Post-rebuttal**] While this may be true, I find the experimental setup fails to properly analyze this trade-off when comparing to the other methods (see **Methods And Evaluation Criteria**).\n\n> [...] show that it consistently shows very competitive performance against the alternative approaches (including TabDDPM - the current state-of-the-art for data quality)\n\nThe authors miss more recent works that have claimed to outperform TabDDPM.\nA non-exaustive list would be: \n\n[1] Alexia Jolicoeur-Martineau et al. Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees. AISTATS 2024\n\n[2] Hengrui Zhang et al. Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space. ICLR 2024\n\n[3] Juntong Shi et al. TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation. ICLR 2025\n\nWhile I do not believe that comparison with these methods is necessary since TabDDPM's performance is, in my experience, comparable, this claim should probably be adjusted.\n\n[**Post-rebuttal note:**] I considered this a minor issue and the authors added more relevant baselines like PATE-GAN and SMOTE", "methods_and_evaluation_criteria": "[**Resolved Post-rebuttal**] In my opinion the selection of benchmark datasets and generative baselines is adequate. I believe, however, that the authors should also compare to other data perturbation approaches, such as approaches that add noise to the data.\n\nThe proposed method generates data by directly manipulating an existing dataset, in contrast to the baselines which are forced to distill a training set down to a more compressed representation which is then used to generate new data.\nThe question of privacy if therefore of central importance and I have two main concerns in this regard:\n\n1. [**Resolved Post-rebuttal**] The choice of the privacy metric. On some datasets we see that the membership inference score is worse than a random classifier. Furthermore, when looking at how this MIA score varies with $n_c$ in Figures 3 and Figures 12-22, we see that it sometimes has little effect and often is not monotonic and varies wildly. All of these observations cast doubts on how adequately this metric can be used to assess privacy.\n2. [**Resolved Post-rebuttal**] Instead of picking a single value of $n_c$, comparison should be made considering both privacy and utility at the same time. This could be accomplished, for example, by making plots similar to those in [1], which show the full trade-off curve between privacy and utility. \nAlternatively, a fair comparison would control for one aspect and measure the other. This approach, however, seems less viable given that the other generative baselines don't necessarily allow for this fine control using a single hyperparameter.\nAs it stands, we are presented with two separate tables where it looks like TabSDS is sometimes achieving higher utility at the cost of less privacy.\n\n\n[1] van Breugel et al. Membership Inference Attacks against Synthetic Data through Overfitting Detection (2023)", "theoretical_claims": "I checked the proof of Theorem 1 and found no issues.", "experimental_designs_or_analyses": "The overall experimental design is sensible in my opinion. \nThe hyperparameters of competing methods are tuned or taken from previous works.\n\nMy main concern is with the choice of metrics and how they are presented (see **Methods And Evaluation Criteria**).", "relation_to_broader_scientific_literature": "This work extends previous work [1] in two directions:\n\n1. It adds a prior step aimed at generating new values for numerical features.\n2. It extends the method (SJPPDS) to work with categorical features.\n\nWhile these extensions are interesting, I still believe that the question of originality arises. \nThe second point seems rather trivial and the impact of the first is not analyzed regarding additional privacy.\nThe main draw of the paper is, in my opinion, the extensive experiments comparing the method to generative approaches\n\n[1] Elias Chaibub Neto. Statistical disclosure control for numeric microdata via sequential joint probability preserving data shuffling", "essential_references_not_discussed": "Not that I am aware.", "other_strengths_and_weaknesses": "[**Resolved Post-rebuttal**] The SJPPDS approach is somewhat *ad-hoc* and does not come with any formal privacy guarantees, unlike other perturbation approaches.\nIt is unclear to me why one would opt to use it instead of simpler methods such as adding noise to the data.\nIn my opinion, some comparison with this type of approach is crucial to prove the value of the proposed method.\n\nThe Appendix includes additional reproducibility details and exhaustive analysis of the results on a dataset-by-dataset basis and is one of the strong points of the paper.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "- [**Resolved Post-rebuttal**] How would this method compare to other perturbtation approaches based on adding noise to data? \n- [**Resolved Post-rebuttal**] What do the privacy-utility trade-off curves look like for both approaches? \n- [**Resolved Post-rebuttal**] Why would I prefer TabSDS over the simpler option?\n\n[**Post-rebuttal Note:**] The authors have provided convincing evidence that their method outperforms simpler approaches like noise addition. While the results against SMOTE and particularly TabDDPM are much more mixed and it seems to me that the latter generally achieves a better trade-off than those made possible by TabSDS, I can see the value in the alternative proposed approach.\nAs a result, I have raised my score from a 2 to a 4.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper performs synthetic data generation by sequentially shuffling features, not training a generative model. The authors provide a proof on how the joint probability distribution is captured by this process, and compare their approach to generative models in terms of fidelity and privacy.

Reviewers noted interest in the non-parametric approach, but asked for more complete benchmarking against prior work with expanded metrics that focus on privacy. These aspects were provided in the rebuttals. A majority of deficiencies raised by reviewers were addressed satisfactorily, and reviewers found the theoretical aspects sound. The addition of existing non-parametric baselines like SMOTE helps to ground the work. Some remaining weaknesses are that the main baseline method TabDDPM is likely out of date and no longer SOTA, as was originally claimed in the abstract and in the paper. I concur with Reviewer r8L7 that these claims should be toned down, and that work in generative modelling since the introduction of TabDDPM should be cited and discussed, and baselined against if possible. Given that the proposed method is non-parametric, notably different from deep generative models like TabDDPM, it may serve a very different role. Hence, it does not necessarily need to be SOTA compared to DGMs, and I can overlook this weakness to recommend acceptance.
Decision: Accept (poster)