TabEBM: A Tabular Data Augmentation Method with Distinct Class-Specific Energy-Based Models
Authors: Andrei Margeloiu
Xiangjian Jiang
Nikola Simidjievski
Mateja Jamnik
Venue: NeurIPS 2024 poster (2024)
Keywords: tabular data
data augmentation
synthetic data generation
energy based model
Primary area: machine_learning_for_other_sciences_and_fields
TL;DR: We introduce a new data augmentation method for tabular data, which trains class-specific generators.

Abstract: Data collection is often difficult in critical fields such as medicine, physics, and chemistry, yielding typically only small tabular datasets. However, classification methods tend to struggle with these small datasets, leading to poor predictive performance. Increasing the training set with additional synthetic data, similar to data augmentation in images, is commonly believed to improve downstream tabular classification performance. However, current tabular generative methods that learn either the joint distribution $ p(\mathbf{x}, y) $ or the class-conditional distribution $ p(\mathbf{x} \mid y) $ often overfit on small datasets, resulting in poor-quality synthetic data, usually worsening classification performance compared to using real data alone. To solve these challenges, we introduce TabEBM, a novel class-conditional generative method using Energy-Based Models (EBMs). Unlike existing tabular methods that use a shared model to approximate all class-conditional densities, our key innovation is to create distinct EBM generative models for each class, each modelling its class-specific data distribution individually. This approach creates robust energy landscapes, even in ambiguous class distributions. Our experiments show that TabEBM generates synthetic data with higher quality and better statistical fidelity than existing methods. When used for data augmentation, our synthetic data consistently leads to improved classification performance across diverse datasets of various sizes, especially small ones. Code is available at https://github.com/andreimargeloiu/TabEBM.

TabEBM: A Tabular Data Augmentation Method with Distinct Class-Specific Energy-Based Models
Andrei Margeloiu', Xiangjian Jiang', Nikola Simidjievski"., Mateja Jamnik' 'Department of Computer Science and Technology, University of Cambridge, UK 2PBCI, Department of Oncology. University of Cambridge, UK {am2770, xj265, ns779, mj201]&cam.. 1@cam. ac.
Abstract
Data collection is often difficult in critical fields such medicine, physics, and chemistry, yielding typically only small tabular datasets. However, classification methods tend struggle with these small datasets, leading to poor predictive per- formance. Increasing the training set with additional synthetic data, similar to data augmentation in images, commonly believed to improve downstream tabular clas- sification performance. However, current tabular generative methods that learn ei- ther the joint distribution p(x, y) or the class-conditional distribution p(x y) often overfit small datasets, resulting in poor-quality synthetic data, usually worsening classification performance compared to using real data alone. To solve these chal- lenges, introduce TabEBM, novel class-conditional generative method using Energy-Based Models (EBMs). Unlike existing tabular methods that use a shared model to approximate all class- consscondiiional densities, our key innovation is to create distinct EBM generative models for each class, each modelling its class- speciicc data distribution individually. This approach creates robust energy landscapes, even in ambiguous class distributions. Our experiments show that TabEBM generates synthetic data with higher quality and better statistical fidelity than existing methods. When used for data augmentation, our synthetic data consistently leads to improved classification performance across diverse datasets of various sizes, especially small ones. Code is available at https: //github.. com/ andreimarggloiu/Tabee.
Introduction
Many scientific domains within medicine, physics, and chemistry often rely on intricate and challenging data acquisition procedures [5, 50, 4, 32, 76, 12] that typically render small- size tabular datasets [5, 46]. Using these to train machine learning models that can aid in tasks such disease diagnosis [52, 37], ma- terial property prediction [35], and chemical compound classification [11], lead to poor performance [74, 52, 37]. In the case of learn- ing tasks which leverage image and data, standard remedy to address performance issues due data scareity employing data augmen- tation techniques [72, 73, 60, 71] that generate additional synthetic samples from existing data.
Inverse
Efficiency
TabEBM (Ours)
19K
GOGGLE
ARF
TabDDPM
KS test
ce. 08 a1 66
Utility
NFLOW
TVAE
SMOTE
DCR
6-gressmoc
Figure 1: Evaluation of TabEBM and other state-of-the--at tabular generative methods across six key metrics (larger area indicates bet- ter performance). The results demonstrate that TabEBM excels in data augmentation (utility), with a larger area than all other methods.
"qqual contribution.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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TabEBM
Real data (input space)
Class-specific EBMs
Class-specific sampling p(xly blue) -Banl)))
Synthetic data
p y
blue)
EBM Ebuue (.)
EBM Ered (-)
p(xly red)
p(xly rod] xe Bmsla))
Figure 2:
An overview of Ta We learn distinct class-specific Energy-Based Models (EBMs)
Exmee (x) and (x) exclusively on the points of their respective class. Each EBM approximates a canssconniiional distribution p(xly), TabEBM allows synthetic data generation by sampling from the estimated distributions for each class p(x = blue) and p(xly = red).
However, applying data augmentation to tabular data introduces additional challenges. as tabular datasets are often very diverse and lack explicit symmetries [8], such as rotations or translations seen in images. Consequently, existing tabular data augmentation methods often yield mixed results and can even degrade model performance [51, 71, 48], hindering their widespread adoption.
Tabular augmentation typically involves training generative models to approximate either the joint distribution p(x, y) [85, 24] or the class-conditional distribution p(xly) [85, 42, 83, 47, 48]. A key challenge of joint distribution methods is maintaining the original training label distribution, as sampling from such generators can produce label distributions that deviate from the original and even fail to generate data for specific classes (see Appendix C for an example). These issues compromise the effectiiveness of data augmentation [51] by undermining the label accuracy and distribution. On the other hand, while class-conditioaal models that learn p(x(y) preserve the stratification of the original data, they often employ shared model to represent all class-conditional densities. This, however, can lead to overfitting, particularly in imbalanced datasets where the model may prioritise more frequent classes [21], ignoring unique features needed for generating label-invariant samples. Additionally, in datasets with limited data, this can lead to mode collapse [68, 70J, where the model does not effectively capture the diversity of each class [70], and thus tends to perform poorly in multi-class setting.
To address the challenges of class-conditional tabular generation, we introduce TabEBM (Figure 2), a new method for tabular data augmentation utilising Energy-Based Models (EBMs). Our method introduces two innovations: (i) Distinct class- class-specific models: TabEBM constructs collection of individual models- one for each class which, by design, enables learning distinct marginal distri- butions for the inputs associated with each class. This, in turn, enables performing data augmentation while maintaining the original label distribution. (ii) Generative models: we build novel class-specific generators that produce high-quality synthetic data even from extremely few samples. Specifically, we create surrogate binary classification task for each class and fit it with pre-trained tabular in-context classifier. We then convert the binary classifier into an EBM, generative model, without additional training. Using class-specific EBMs makes the energy landscape more robust to class overlaps, compared to using a single shared EBM to approximate the class-conditional distribution.
Our contributions can be summarised as:
Technical:
We propose TabEBM, which is the first generative method to create class-specific EBMs, learning the marginal distribution for each class separately.
Empirical: We present the first comprehensive analysis of tabular data augmentation across different dataset sizes and use cases beyond predictive performance. Our analysis compares TabEBM with eight leading tabular generative models across various datasets, demonstrating that TabEBM consistently improves data augmentation performance on small datasets, while our generated data demonstrates better statistical fidelity and privacy--reserving properties (Figure 1).
Library: We release TabEBM as an open-source library, available at https://g/ httptttbbbb.../////// thub. com/ andreimares mnddrimarrgeloi/Taaaeen Our library enables off-the-shelf data generation and data augmenta- tion on any tabular dataset without requiring training. Further details are available in Appendix B.5.
2

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2 TabEBM
Notation. We address classification problems with C classes, denoted by y {1,2,.... .,, C, Let ((x(", ,,)) represent dataset of N samples, each being D-dimensional vector x(1) RR,, with corresponding label y; y: For each class V, we define X. fx(()) y/s c} as the subset of samples labelled with class c. Let fo(-) denote a classifier. The expression fo fx(x)(t) represents the (unnormalised) logit assigned to the class y for the input
2.1 Preliminaries on Energy-Based Models
An Energy-Bann -Based Model (EBM) [43] defines probability density function po px(x) through an energy function E(x). Specifically, the model posits that p(x) x e E(xx) where E(x) represents the unnormalised negative log-density of the input In this framework, lower energy values correspond to higher probability densities. This relationship allows EBMs to model distributions by learning to assign lower energy to more probable configurations of x and higher energy to less probable ones.
An important observation is that energy- based models utilise the same model architectures as standard classification models [29]. Typically, the logits [o(x)[y) [y] from a classification model define discriminative distribution through the softmax function, expressed as po(y)x) softmax (xx(xx((x))))))))))x [y]). Intriguingly, these same logits can be reinterpreted to define an energy-based model for the joint dis- tribution p(x. y). This achieved by setting the energy function to Exx, y) - fx(x). Furthermore, the energy function for the marginal distribution p(x) is obtained by marginalising over p(x, y). resulting [xx) LLgSSum fo [x)))
Such an energy-basse based model, trained with EBM-specifii protocols on multiple classes, is typically used classifier, demonstrated on several computer vision tasks in [29]. In contrast, in this work our focus is the opposite: we propose employing trained classifiers, one for each specific class, as a generative energy-based model for the class-conditional distributions p(xly). We apply our TabEBM method for generative tasks on tabular data.
2.2 Distinct Class-Specific Energy-Based Models
TabEBM is class-conditional generative model p(xly) implemented using set of EBMs, {E1 (x), Eg (x),..... ...., (x)x) Our approach assumes that the class-conditional density p(xly = c) is best modelled using its class-specific data X,- Thus, for each class we construct class-specific EBM, Ex(x,, using only the data from that class, X,s such that p(x|y = c) x exp(-EE.(6)
We derive each class-specific EBM (x) ) by training a classifier on novel task and reinterpreting its logits. Specifically, for each class c, we propose a surrogate binary classification task to determine if a sample belongs to class c by comparing Xe against a set of surrogate negative samples Xa which we show in Figure 3. Specifically, we generate the negative samples at the corners of a hypercube in RD_ For each dimension d, the coordinates of negative sample are either a agg or neg dd, where a dist is fixed constant and oa the standard deviation of dimension d. For example, in R3, a negative sample might have coordinates dist dist Placing the negative samples at the corners of hypercube ensures they are easily distinguishable from the real data, which is crucial for an accurate energy function (see Appendix 1.). This placement is also robust to variations in the number and distance of the negative samples (see Appendices 1.1.2 and D.1.3).
samples negative samples 2099
neg
neg neg -a a T3).
The class-specific energy function Ex(x) from the surrogate binary task, where the blue region repre- sents low energy (i.e., high data density). Placing the neg- ative samples in a hypercube distant from the data results in (1) accurate energy function.
Figure 3:
We create the combined dataset D. for the surrogate binary classi- fication task by labelling X, and x.meg as O:
D. = (X, U ATTE, negg (1)12d (00
We then train binary classifier f)(-) D. and use it to construct the class-specific energy Ex for class e. To do this, we reinterpret the logits (f}(x) [0), [x)) of the trained binary classifier components of an approximated joint distribution for the surrogate binary task:

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Pc(x,0) 0) exp(Sā(x)(0
Pe(x,1)= exp(J)(x)(1))
(Z is the normalisation constant)
Z
Next, we derive the approximated distribution Pe(x) by marginalisation:
Pa(x) = Pe 0) + Px(
exp(fx (x) (0]) (x
exp (log (exp (f/ (x) [0]) + cxp(ff(x)(L))
Z
+ Ex(x) - log (exp( + exp(f((x)(1))
(TabEBM class-specific energy)
(3)
For the binary classifier (.) in the surrogate binary classification, we TabPFN [33], a pre-trained tabular in-context model. Note that TabPFN is intended for inference only, with no updates to its parameters (see Section 4 for more details about TabPFN), In this context, "training" the TabPFN classifier is analogous to the K-Nearest Neighbour algorithm, which simply performs inference based on a training dataset provided the model. We apply TabPFN multiple times on separate datasets {D1. Dz...... } to obtain multiple classifiers fe f 4C1. explore why reinterpreting TabPEN's logits, trained on our surrogate binary tasks, can be useful for estimating energy function. We emphasise that TabEBM is a general method, capable of using any gradient-base based classifier that computes logits (using Equation (3)), and is not limited to TabPFN.
In Section 3.4, we
Generating data with TabEBM involves two steps. First, we sample a class e from the empirical distribution ~ p(y). Then, we sample data point from the conditional distribution X p(xly = c) approximated by the class-specific energy-based model (x), as outlined in Algorithm We employ Stochastic Gradient Langevin Dynamics (SGLD) [84] to perform this sampling. SGLD is an efficient method for high- nigh-dimensiinal data, combining stochastic gradient descent (SGLD) with Langevin dynamics. The update rule for SGLD each iteration
7 V(()) + c,, 6 ~~,00,
X X
2
where a Gaussian noise term 6, introduces randomness into the sampling process, enhancing the exploration of the distribution. In practice, the step size and the noise standard deviations are often chosen separately, resulting in biased sampler that allows for faster training. Appendix D.2 further shows that TabEBM is stable to hyperparameters for the sampling process.
In our method, SGLD performs iterative augmentation. We start by sampling close to real data and iteratively adjust these synthetic data points, steering them towards regions of higher probability under the learned energy model. TabEBM enables sampling from any specified class distribution, including the original class distribution, which is crucial for data augmentation.
Algorithm 1 TabEBM sampling from Class-Specifie EBM Ex(x)
Input: Training data X for class c, step size Csup, noise scale Onvises initial perturbation Tsunt, number of steps T Set of synthetic samples for class
Output:
Initialise a surrogate binury classification task and train the model
1: Assign new labels to the samples X₂ from class c, setting them to class 1
2: Generate set of surrogate negative samples X and assign them class 0 lahels
3: Train a binary classifier fū on the dataset D. = (Xa U 2 {1} &el U (0) 14!0)
Synthesise samples using Stochastic Gradient Langevin Dynamics (SGLD)
sythh by sampling from (Xx,, (m 4: Initialise synthetic data points X
5: for each iteration = 0, 1, T
1 do
6: (x/tt)) log exp Syath (0)) exp(f6 (11)
7: x x
synhh synh Clsap v (x; Smih + N/ a
end wath
9: return x as the generated synthetic data for class c

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3 Experiments
We evaluate TabEBM by focusing on four research questions:
Data Augmentation Improvement (Q1, Section 3.1): Can TabEBM generate synthetic data that improves the accuracy of downstream predictors via data augmentation?
Statistical Fidelity (Q2. Section 3.2): Can TabEBM generate synthetic data with high statistical fidelity (i.e., with similar distributions to those of real data)?
Privacy Preservation (Q3, Section 3.3): Can TabEBM generate synthetic data that finds a competitive trade-off between downstream performance and privacy preservation?
Understanding TabEBM's energy formulation (Q4, Section 3.4): Why is TabEBM's class- specific energy effective, and how do the proposed surrogate tasks influence this?
Datasets. We utilise eight open-source tabular datasets from OpenML [7] across five domains: Medicine, Chemistry, Engineering, Language and Economics. As TabPFN utilises many small-size OpenML. datasets in its meta- validation [33], it can lead to data leakage when evaluating TabEBM. Therefore, to provide fair comparisons, we select six additional leakage-free datasets from UCI [22]. These diverse datasets contain 7 to 77 features and 698 to 5500 samples across 2 to 26 classes. Five datasets contain both numerical and categorical features, while the remaining are numerical only, We further enlarge the evaluation scope by varying the degrees of data availability (i.e., Nreat), leading up to 33 different test cases for the eight OpenML datasets. Appendix B.I provides detailed descriptions.
Benchmark generators. We compare TabEBM against eight existing tabular data generation methods of eight different categories: (i) standard interpolation method SMOTE [13]; (ii) a Variational Autoencoders (VAE) based method TVAE [85]; (iii) a Generative Adversarial Networks (GAN) method CTGAN [85]: (iv) a normalising flow model Neural Spine Flows (NFLOW) [24]; (v) a diffusion model TabDDPM [42]: (vi) tree-based method Adversarial Random Forests (ARF) [83]; (vii) Graph Neural Network (GNN) based method GOGGLE [47]; and (viii) Prior-Data Fitted Networks (PFN) based method TabPFGen [48]. Furthermore, we also include "Baseline" model, where no data augmentation is applied (i.e., only real data is used to train downstream predictors). In Appendix B.6, we detail the settings used for TabEBM and all other generators.
Downstream predictors. We select six representative downstream predictors, including three standard baselines: Logistic Regression (LR) [16], KNN [27] and MLP [28]; two tree-based methods: Random Forest (RF) [10] and XGBoost [14]: and a PFN method: TabPFN [33].
General experimental setup. For each dataset of N samples, we first split it into stratified train and test sets. We create large test sets to reduce the likelihood that the model's 's performance is accidentally inflated due to a small, unrepresentative set of samples [69], and thus the test size is computed via Nustt min (>) 500). The full train set approximates the upper bound of the quality of synthetic data, and we call this set "oracle". We subsample the full train set to simulate different levels of data availability, thus the subset size Necal varies over {20, 50, 100, 200, 500]. We split each subset into stratified training and validation sets with a ratio of 4:1. We provide detailed descriptions of data splitting in Appendix B.2 and preprocessing in Appendix B.3. We repeat the splitting ten times, summing up to 10 runs per subset size. The reported results are averaged by default over ten runs on the test sets. When aggregating results across datasets, we use the average distance to the minimum (ADTM) metric via affine renormalisation between the nop-performing and worse- performing models [30, 54]. We provide the evaluation results averaged over six downstream predictors for a general conclusion, and the fine-grained numerical results for each predictor are in Appendix D.
Data augmentation setup. Given Nical real samples, we first train generators on the real training data and then generate/ Nayn synthetic samples. For training the downstream predictors, we expand the real training split by adding the synthetic samples. The real validation data is used for early stopping, and the real test set is used for evaluating the predictor's 's performance. The optimal Nayn remains an open problem for tabular data [51, 71, 31]. Prior works [47, 48] mainly use synthetic sets with equivalent sizes to the real sets (i.e., Nreal Nayn). However, we observe that N = Nsyn can lead to highly unstable results, especially on small datasets that we investigate. Recent work has used different Nayn for various generators, such as by applying post-processing [31, 71]. In this work, we want to provide a head-to-head comparison of the effect of data augmentation across subsampled datasets of varying sizes Nr E [20, 50, 100, 200, 500). Therefore, we perform data augmentation with large synthetic set (Ney = 500) across all splits, and the synthetic data has the same class distribution as the real training data. We provide an illustrative figure of the data splitting setup in Appendix B.2.
5

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Table 1: Classification accuracy (%) aggregated over six downstream predictors, comparing data augmentation on eight real real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. higher rank implies higher accuracy. Note that "N/A" denotes that a specific generator was not applicable, and the rank is computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample size. Our method, TabEBM, consistently outperforms training on real data alone, and achieves the best overall performance against Baseline and benchmark generators.
Baseline (Real data)
Datasess
Now
SMOTE
TYAE
CTGAN
NPLOW
TEMDDPM
GOGGLE
TahPPGien
TabEBM
20
28.14
NIA
21,18:144
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21.30
33.25 22.40 24.82
33.84
50
54.52
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35.37 36.32
11.9
37.53 pm
54.45 1Tw.
55.91
protein
67.83
23.25_774
59.28
57.64
52.57
56.37290
57.01
21.53
200
81 181661110
85 65
76.42.77
74
72
75
76,86
74407
73.57g47
84.95
86.14g50
500
93.49:5528
94.7 24.73
92.24
91 91.48
90.44
90.62250
91.79
91.31
94.8721.0
98.18
28.30+1229
21.32+4406
18.19
17.30-31
21.75+224 15.35
16.70
36.7241.0
37.13
53.69 4304
51 1744
37,96 37,96:4445
a5.09
31.94:330
35.99
40.32
33.56.2240
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55.11
56.57 27.12
fourier
100
63.70
64.10
50.46
49.26
52.79
11.13
41.93
63.86
65:21
At 10 classes
200
70.99 14:04
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62.17
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19.15
68.05
62.53
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71.55
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500
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78.11
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80.11 22:3
500
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82.85
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energy
100
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18.56 18.60
10. 14-2am
18.841
10.55
11.99
19.9
15.46:154
17.65
N/A
N/A 23.98
31.24
200
35.99 1399
27.65
27.77
g8937
29.50gmum
29.57
28.95
NIA
41.28 1766
collins
100
11.44
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8.38
2.1
7.93
12.672216
7.53
9.21
N/A
13.07 #2:1
200
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11,37,1
10.74.177
15.39
10.71
14,30g74
N/A
1730
12.40
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55.32:x21
24.80
62.27
55.65-2055
22.94
N/A 78.90 27:5
texture
200
100
$2. 62.42mmma
37,54
84.35
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78.37
66.00
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81.94
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84.67
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16.34
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N/A
89.77 2517
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Average rank
3.30
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6.79
7.48
2.94
6.39.241
6.94
7.762210
3.18
1.21 22.4
3.1 Data Augmentation Improvement (Q1)
We evaluate the effect of using synthetic data for data augmentation by comparing the balanced accuracy of downstream predictors before and after augmentation. Typically, higher classification accuracy (i.c.. ACCGenerator) and accuracy improvements (i.c., ACCGencrator - ACCBaseline >> 0) demonstrate the effectiveness of the synthetic data for data augmentation.
TabEBM effectively improves downstream performance across sample sizes, especially for very low-sample-size regimes. Table and Figure 4 (Left) show that TabEBM exhibits competitive performance in data augmentation, generally achieving the highest downstream accuracy and average rank across most datasets and sample sizes. Notably, TabEBM is the only generator that consistently improves performance across sample sizes. A key observation is that most modern benchmark generators underperform even the Baseline, indicating poor approximated distributions in the low-sample-size regime. Moreover, TabEBM achieves the largest overall performance improvement on six leakage-free UCI datasets, further supporting its effectiveness (see Appendix D.5.2 for details).
Furthermore, TabEBM is the most widely applicable method among the top three competitive generators on the considered datasets: (i) SMOTE requires at least two samples per class for interpolation, and thus it is not applicable for some datasets, such as the "protein" dataset (Nreal = 20); (ii) TabPFGen cannot scale up more than ten classes, such as the "collins" dataset. In addition, TabEBM can stabilise downstream performance, especially when real data is very scarce (Nrral = 20): TabEBM leads smaller standard deviations than Baseline on seven out of eight datasets.
TabEBM effectively improves downstream performance across any number of classes, especially for more than ten classes. Figure 4 (Right) shows that TabEBM consistently outperforms the

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Normalised accurasyy impt improvenent (16)
25
SMOTE TWAE
GOOGLE
GOOGLE
TAADPPM ARP
25
TVAE
TADDPM
TAAPPG
CTGAN
TAAFIM (Due))
CTITAN
ARP
TabiRW (Qun)
-25
-25
Baseline
100
200
300
400
500
-50
At most 10
More than 10
Number of real samples
Number of classes
Figure 4: Mean normalised balanced accuracy improvement (%) across different sample sizes (Left)) and across datasets with varying numbers of classes (Right). Because TabPFGen is not applicable for datasets with more than ten classes, we plot short bars at zeros for visual clearance. Positive values indicate that the generator improves downstream classification performance. TabEBM generally outperforms benchmark generators across varying sample sizes and number of classes.
Baseline with notable improvements, particularly in datasets with more than ten classes. In contrast, an increased number of classes tends to cause a performance degradation in the benchmark generators.
TabEBM is robust on imbalanced datasets. For the three binary OpenML datasets (i.c.. "biodeg", "steel" and "stock"), we adjust the class distribution in the training data vary the class imbalance, while keeping the test data fixed. Figure shows that TabEBM consistently outperforms Baseline, while the other generators exhibit performance degradation as data imbalance increases.
TabEBM is computationally efficient. Figure 6 shows the trade-off off between accuracy and the time needed for generating stratified synthetic data (for data augmentation). We measure the total duration
of (i) training the model and (ii) generating 500 synthetic samples. The results show that TabEBM is practical, it achieves higher downstream accuracy with lower time costs.
Nornalised nocuracy improveent (%%
Nomualied accursey impercennnn (5)
10.0
SMOTE
TahDIPM
TabEBM (Ours)
TVAE
TahiFGGen
7.5
CTGAN
TabEuM (Ours)
TahPPion
5.0
SMOTE
2.5
TrADDPM
0.0
IVAL
ARU
CTGAN GOOGLE
-25
20
NFLOW
5.0
500
1000
1500
2000
0.0
0.3 0.4 0.5 Ratio #Minority: (#Minority + #Majority)
0.1
0.2
Data augmentation time (5)
Figure 6: Median data augmentation time vs. mean normalised balanced ac- curacy. TabEBM achieves higher down- stream accuracy while typically operating 3-30 times faster than most other methods.
Figure 5: Mean normalised balanced accuracy im- provement (%) on imbalanced datasets. TabEBM consistently outperforms the Baseline and other gen- erators across different levels of data imbalance.
3.2 Statistical Fidelity (Q2)
We evaluate the fidelity of synthetic data by measuring the similarity of synthetic data to real train data and to real test data (Figure 7). We evaluate this similarity via (i) average inverse of test (KS
the Kullback-eeibler Divergence (inverse KL) [17], (ii) p-vuuue of Kolmogoro- test) [39] and (iii) p-value of Chi-squared test (x2 test) [55]. For full numerical results, including x2 test, see Appendix D.6. For all three metrics, a bigger value denotes that synthetic data is more likely to have the same distribution as real data.
In Figure 7 (al&a2), TabEBM consistently exhibits the highest accuracy and distribution similarity between real train data and synthetic data, indicating that TabEBM learns the distributions of real train data better than benchmark generators. In Appendix D.6, we further show that TabEBM remains the most competitive method in similarity between real test data and synthetic data. This indicates that TabEBM can extrapolate beyond real train data and thus generate synthetic data from a more
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10
Noemaliond necumay change (96
10-
TabEuM (Ours)
TabEBM (Oors)
TabLuM (Ours)
TabEBM (Ours)
SMOTE
SMQTE
TabPFGGes
0
TahPeCian
JahPPGen
J JAPRiien
SMOTE
SMOTE
Nomalted necurncy
10-
JahDDPM GOGGLE
-10
JobDDPM GOGGLE
-00
JVAE
ARF
-20
ARAR
TVAE CTGAN
ARF
TVAE
RF NFLOW
UTGAN RADDPM
CTGAN
J.bDDPM
NFLOW
NTLOW
-20
GOGGLE
GOGGLE p
0.0 0.2 0.4 06 0.8 1.0
0.6
0.8
09
1.0
0.2 (b1)
0.4
0.5
(a1) Inverse KL (main, syn)
(a2) KS test (train, syn) f
DCR (train, syn)
(b2) S-presence (train, syn).
Figure 7: &al):)): Median inverse KI. and KS test vs. mean normalised balanced accuracy im- provement (%) between real train data and synthetic data. (b1&h2): Median DCR and 5-presence vs. mean normalised balanced accuracy change (%) between real train data and synthetic data. Note that "accuracy improvement" is for data augmentation, and "accuracy change" for data sharing. Complete results with standard deviations are in Appendix D.4. TabEBM generates high-fidelity synthetic data that can also be used for privacy preservation.
general distribution that aligns with both train and test data. This extrapolation ability also explains why TabEBM can outperform Baseline via data augmentation (Section 3.1).
3.3 Privacy Preservation (Q3)
More broadly, data privacy is a critical concern for organisations and governments handling sensitive data [75]. crivacy-presevvin synthetic data allows researchers and practitioners to bypass ethical and logistical issues while enabling model training and testing [38]. We further explore the use of RabEBM-generater data for data sharing, where only synthetic data is accessible for downstream users [75, 89, 86, 23, 42]. In this case, downstream models are trained exclusively on synthetic data.
Specifically, we evaluate synthetic data via three metrics: (i) balanced accuracy of downstream predictors trained with only synthetic data (i.e., train-on-synthetii,, test-on-real [85, 42, 87]); (ii) me- dian Distance to Closest Record (DCR) [88], where a greater DCR denotes synthetic data is less likely to be copied from real data; and (iii) d-presense [62], where a smaller value denotes lower re-identification risk for real data from synthetic data. Full numerical results are in Appendix D.7.
Figure 7 (b1&b2) shows that TabEBM consistently finds a better trade-off between accuracy and privacy preservation. Notably, the "train-on-symthette test-on-real" scenario poses a greater challenge for generators in achieving high accuracy because real data is inaccessible for model training and data augmentation. Despite this difficulty, TabEBM is the only generator that surpasses the overall performance of training on real data (i.e., Baseline). The relatively high DCR for TabEBM indicates that it can extrapolate beyond real train data, aligning with the finding that TabEBM's S synthetic data is statistically similar to real test data (Section 3.2). These results further suggest that TabEBM learns the general distribution of real data, and can generate high-quality synthetic data suitable for various purposes, including privacy preservation.
3.4 Why is TabEBM effective for estimating Energy-Base -Based Models? (Q4)
Having established that TabEBM excels in data augmentation, we explore why clas- sifier logits can be useful when reinter- preted as a class-conditional energy func- tion. Figure 8 shows the logit distribu- tion of TabPFN trained on surrogate binary tasks and the corresponding energy fune- tion of TabEBM (with TabPFN as the bi- nary classifier) as the Euclidean distance from the real data increases.
15.0
Unnorm density (x1000)
150
12.5-
125
Logit value
10.0
200
7.5-
50-
2.5
Logt PAT brrea Cata
25.
5
15 20
1'5 20
Distance from the real data
Distance from the real data
Figure 8: (Left) Logit distribution of TabPFN trained on our surrogate binary tasks increasing distances from the real data (on "steel"). (Right) The correspond- ing unnormalised density approximated by TabEBM. TabEBM assigns higher density closer to the real data.
We found it essential to place the nega- tive samples far from the real data, since TabPFN, which is pre-trained to approxi- mate Bayesian inference [33], has its confi-
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dence influenced by the distance from the training data [53]. Figure 8 (left) shows that TabPFN outputs high logit values near the real data. As the distance from the real data increases, the logit [ decreases smoothly until the two logits become similar, making the classifier uncertain (because the class probabilities become equal). Figure 8 (right) shows that TabEBM's inferred density drops significantly as the maximum logit decreases, because Px(x) x (exp(](x)(0) + (xp([((x((1] from Equation (3), Since SGLD sampling performs gradient ascent on the density, the TabEBM --gnerrtted samples will be close to the real data. These findings are consistent across datasets (see Appendix D.3), where TabPFN's logits remain positive, with similar ranges and a relatively constant sum as distance increases, warranting further investigation. Overall, TabPFN's for inferring accurate energy functions within our TabEBM framework. Since TabEBM can be paired with any other gradient-basee classifier that produces logits, we leave these extensions for future work.
eestance-based uncertainty is useful
4 Discussion & Related Work
Section 3 showed that TabEBM efficiently generates high-fidelity data that can effectively improve the downstream performance via data augmentation. In Table 2, we further provide summary of tabular data generative models analysed from three important perspectives: (i) Training: the type of distribution that the generators learn (crucial for preserving the original training label distribution), and the training costs associated with learning; (ii) Generation: do the generators employ class-specific models (reflecting their capability to capture unique features essential for label-invariant generation). and do models support stratified generation (crucial for effective data augmentation); (iii) Practicabilityy: the scalability of the generators with respect to the number of classes (a common requirement in real-world multi-class tasks), and consistent downstream performance improvement across different class sizes.
Generative Models for Tabular Data. The common paradigm for tabular data generation is to adapt Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) [85, 63]. For instance, TableGAN employs a convolutional neural network to optimise the label quality [63], and TVAE is introduced in [85] as a variant of VAE for tabular data. However, these methods learn the joint distribution and thus cannot preserve the stratification of the original data (Appendix C). CTGAN [85] refines the generation to be class-conditional. The recent ARF [83] is adversarial variant of random forest for density estimation, and GOGGLE [47] enhances VAE by learning relational structure with a Graph Neural Network (GNN). Some recent work focuses on generation with denoising diffusion mod- els [42, 87, 40, 44). For instance, TabDDPM [42] demonstrates that diffusion models can approximate typical distributions of tabular data. Although these caass-oonditionll models can preserve the label distribution, they struggle to outperform Baseline and standard SMOTE in data augmentation [71, 48].
We attribute the performance degradation in current class-conditional models to their reliance single shared model to approximate all conditonnii densities. For instance, another promising generative approach uses pre- pre-trained models like Prior Data Fitted Networks (PFNs), and the recent TabPFGen [48] adapts such models into one shared conditonnii generator. However, TabPFGen's 's shared generator can lead to inaccurate density estimates, particularly in high-noise and class- imbalance situations (see examples in Appendix C). As noise increases, TabPFGen's 's inferred densities fluctuate significantly and diverge from the true data distributions. In contrast, TabEBM uses class- specific EBMs to model each class's 's marginal distributions, and the results in Appendix C reveal that our design choice reduces the impact of noise and data imbalance. TabEBM focuses approximating and generating for one class at a time, remaining unaffected by noise from other classes. Overall, our results demonstrate that TabEBM consistently improves performance across different datasets and sample sizes, outperforming TabPFGen. Moreover, TabPFGen is limited in usability (e.g., it supports only up to ten classes), while TabEBM scales to any number of classes.
In a broader context, some recent work attempts to adapt Large Language Models (LLMs) for tabular data generation [25. 71, 9]. However, data contamination is an inherent issue with such LLMd- models [19, 36, 18, 49]. As the pre-training data is not typically open-source, these models can have unfair advantages in downstream tasks (i.e., the full real dataset, including the real test data, may have been used for pre-training). Therefore, in this paper, we focus on models without support from LLMs, thus avoiding potential biases from data contamination.
Data Augmentation (DA) for Tabular Data. DA is an omnipresent technique in computer vision and natural language processing [82, 73, 72, 60, 26, 2]. However, DA for tabular data remains

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Table 2: Comparison of the properties between TabEBM and prior tabular generative methods. TabEBM has novel design rationales of training-frce freee class-specific models, and TabEBM is highly
practicable with wide applicability and consistent accuracy improvement.
Training
Generation
Practicahility
Methods
Category
Learned distribution
Training-free
Class-seciili models
Stratified generation
Unlimited classes
ACC improve
ACC improvee
(% 10 classes)
(> 10 classes)
SMOTE [15]
Interpolation
NIA
NIA
TVAE [85]
VAE
p(x, vt)
X
x
CTGAN [85]
p[x 9)
x
X
NFLOW [24]
Normal. Flows
pix.
X
X
X
X X
TahDDPM [42)
Diffusson
p(x k)
X
X
V
ARF [83]
Random Forest
pix
x
X
X
X
GOGGLE [47]
GNN
p(x M)
X
TabPFFGen [48]
PFN
x(x M)
X
TabEBM (Ours)
PFN p(x ())
underexplored, and existing methods often perform poorly in real-world tasks, sometimes even reduce performance [. Recent studies show that using the same transformations across all classes leads to varied performance impacts [3, 41], indicating that data augmentation effects are class-specific and suggesting that different classes may require distinct augmentations. Given the lack of symmetries in tabular data, we believe this class-dependent effect is even more pronounced. Therefore, we propose TabEBM as a claas--peciffe generative model to produce tailored augmentations for each class.
Prior-fitted Networks (PFNs) for Tabular Data. Recent work proposes to approximate the posterior predictive distribution with transformers [59, 33, 61, 79, 20]. PFNs can be adapted for various pur- poses by pre-training the transformer with corresponding "prior data", and then can make in-context predictions with unseen downstream data. For instance, TabPFN is variant that is pre pre-trained prior designed for tabular data [33]. We note that prior data is different to synthetic data in this paper. Specifically, prior data refers manually crafted fake data (e.g.. y/ = 2xr) with no real-world semantics. In contrast, synthetic data from generators is expected to have the same semantics as real data. In- spired by TabPFN's success in small-size classification tasks, TabEBM converts TabPFN into multiple EBMs that learn the marginal distribution for each class. The training- training-free nature of TabPFN enables Ta to generate high-quality tabular data without introducing extra training costs. Additionally, our class-specific design lets TabEBM surpass TabPFN's s limits and scale to more than ten classes.
Limitations and Future Work. TabEBM is general method that relies classifier, and as such, its strengths and weaknesses are directly tied to this classifier. We used TabPFN because it is well-established open-source pre-trained model for tabular data. Therefore, TabEBM inherits some of TabPFN's 's limitations, particularly in scaling to a larger number of features. TabEBM can handle datasets with over 1000 samples, overcoming TabPFN's 's limitation, it processes one class at time. In Appendix D.5.3, we show that TabEBM outperforms other generators on larger datasets, though the performance gains decrease as the sample size increases. Although we implement TabEBM with TabPFN in this paper, we stress that TabEBM is compatible with any classifier that can be adapted into EBMs, as described in Section 2. As foundational models for tabular data evolve [81], new models capable of handling more features and samples are expected. Integrating them into TabEBM will enhance its ability to manage high dithesiinnii datasets, increasing its versatility and utility. Finally, note that, generators that are limited in modelling multivariate distributions may still perform well on univariate fidelity metrics, which models. However, evaluating their ability to learn more complex, high-order, relationships between features remains an open research question [78], which we leave for future work.
underlying binary
standard approach to evaluating such
Conclusion
We introduced TabEBM, the first tabular data augmentation method that creates class- specific EBM generators, learning the marginal distribution for each class separately. We also provide the first comprehensive analysis of tabular data augmentation across various dataset sizes. Our results demonstrate that TabEBM improves downstream performance through data augmentation on real- world datasets, outperforming other benchmark generators. The statistical evaluation confirms that TabEBM generates high-fidelity synthetic data, particularly for small datasets. We release our method as an open-source library, allowing users to generate data immediately without additional training.
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Acknowledgments and Disclosure of Funding
The authors would like thank Francisco Vargas, Randall Balestriero, and Otilia Stretcu for their insightful discussions and valuable input early in the project. NS and MJ acknowledge the support of the U.S. Army Medical Research and Development Command of the Department of Defense; through the FY22 Breast Cancer Research Program of the Congressionally Directed Medical Re- search Programs, Clinical Research Extension Award GRANT13706 3769913.. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the Department of Defense.
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Appendix
TabEBM: A Tabular Data Augmentation Method with Distinct Class-Specific Energy-Based Models
Table of Contents
A Broader Impact Statement
18
B Reproducibility
18
B.1
Datasets
18
Data Splitting
B.3 Data Preprocessing
B.4
Software and Computing Resources
19
B.5
TabEBM open-source library
20
B.6
Implementation of Generators
20
B.7
Implementation of Downstream Predictors
20
Limitations of Existing Generative Methods
21
D Extended Experimental Results
24
D.I Ablations the distribution of the surrogate negative samples
24
D.1.1 Ablations placing the negative samples
24
D.1.2 Varying the number of negative samples
24
D.1.3 Varying the distance of the negative samples
25
D.2 Ablations on the sensitivity to the hyperparameters of SGLD sampling
25
Distribution of Logits and Unnormalized Density in TabEBM
26
D.4 Complete Trade-off' Figures with Error Bars
27
D.5 Results Data Augmentation
28
D.5.1 Results eight OpenML datasets.
28
D.5.2 Results on six UCI Datasets
34
D.5.3 Results on larger sample sizes
34
D.6 Results on Statistical Fidelity
34
D.6.1
Similarity between Real Train Data Synthetic Data
35
D.6.2
Similarity between Real Test and Synthetic Data
38
D.7
Results Privacy Preservation
41
D.7.1
Downstream Accuracy in Data Sharing
41
D.7.2
DCR Evaluation
48
D.7.3
Delta-presence Evaluation.
49
17

---

A Broader Impact Statement
This paper introduces a novel data augmentation approach, TabEBM, that aims advance the field of machine learning by addressing challenges in the low-sample-sizz regime. Furthermore, TabEBM offers an elegant solution learning the unique features in generating samples for each class, leading to high-fidelity synthetic data that can effectively improve downstream performance. These characteristics can be particularly useful in data-scarce domains like healthcare (e.g., pre-clinical drug evaluation in early-stage clinical trials [6, 58)). Moreover, we also demonstrate that TabEBM is readily applicable for srivacy-preserving data sharing high-stake tasks [89, 77].
TabEBM's impact further extends to enabling broader machine learning applications in data-scarce domains, for instance, facilitating data analysis in clinical scenarios with limited access data collection techniques. Improving the performance of machine learning models in such applications can further foster the uptake of more sophisticated MI approaches and, ultimately, help improve the quality of healthcare [1, 15, 57]. TabEBM can further facilitate research and enhance machine learning accessibility in various communities across societal and scientific domains. To this end, our work has only been evaluated in a strictly research setting. Further applications of our work in scenarios with sensitive data bear some risks. As TabEBM a generative model, training models with the resulting generated samples can bias the downstream model. Therefore, this risk, together with other data privacy risks during downstream deployment, must carefully managed.
B Reproducibility
B.1 Datasets
All eight datasets are publicly available on OpenML [7]. and their details are listed in Table 3. To ensure consistent stratified data-splitting across all datasets, remove classes with fewer than 10 sam- ples. For example, the original "energy" dataset contains 14 classes with fewer than 10 samples, which could result in validation set lacking samples from these classes, leading to unstratified data splitting.
Table 3: Details of the eight woold tabular datasets.
OpenML
Not evaluated in TabPEN [33]
Samples (N)
(D)
Classes
N/D
Samples per class (Min)
Samples class (Max)
At most 10 classes
protein
40966
X
1,080
77
14.03
105
150
fourier
X
2,000
10
26.32
200
200
biodog
1494
X
1.055
25.73
699
X
1,941
1,268
stock
X
105.56
488
More than classes
energy
1472
x
698
9
23
77.56
10
collins
970
26
51.05
17
5,500
B.2 Data Splitting
Figure shows the data splitting setup used across all datasets. Note that data sharing (Section 3.3) shares the same data splitting as data augmentation, except that the "Training set" and "Validation set" containing real data no longer used for training the downstream predictors.
18

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Dataset
Oracie set (l.e,, full train set) Moracle Mtest
Test set
N Wtest
min 500
Subsets
real [200 200,500)
Training set roal
Validation set mal 0.2
Downstream predictors
Predictions
Generator
Synthetic 500
Figure
Data splitting strategies for data augmentation for all datasets.
B.3
Data Preprocessing
Following the procedures presented in prior work [54, 30), perform preprocessing in steps. We first compute the required statistics with training data and then transform it. Firstly, we impute the missing values with the mean value for numerical features and the most mode value for categorical features. Secondly, we convert the categorical features into numerical features equal to Leave-one-out Target Statistic [66, 56]. Next, perform Z-score normalisation for each feature. Specifically, we compute each feature's mean and standard deviation in the training data and then transform the training samples have mean of zero and a variance of one for each feature. Finally, we apply the same transformation to the validation and test data before conducting evaluations.
B.4 Software and Computing Resources
Software implementation. (i) For generators: We implemented TabEBM using PyTorch 1.13 [64], an open-source deep learning library with BSD licence. We implemented SMOTE with Imbalanced- learn [45], an open-source Python library for imbalanced datasets with an MIT licence. For other benchmark generators, used their open-source implementations in Synthcity [67], library for generating and evaluating synthetic tabular data with an Apache-2.0 license. (ii) For downstream predictors: We implemented TabPFN with its open-source implementation (https: //tg://gtttbb com/ Tatop)/TabPFM), We implemented the other five downstream predictors (i.e., Logistic Regression, KNN, MLP, Random Forest and XGBoost) with their open-source implementation in scikit-learn [65], an open-source Python library under the 3-Clause BSD license. (iii) For result analysis and visual- isation: All numerical plots and graphics have been generated using Matplotlib 3.7 [34], Python- based plotting library with a BSD licence. The model architecture was generated using draw.io (https://gg gi thub. com/ jgraph/drawio)) free drawing software under Apache License 2.0.
We ensure the consistency and reproducibility of experimental results by implementing a uniform pipeline using Py Torch Lightning, open-source library under Apache-2.0 licence. We further fixed the random seeds for data loading and evaluation throughout the training and evaluation process. This ensured that TabEBM and all benchmark models were trained and evaluated on the same set of samples. The experimental environment settings, including library dependencies, are specified the open-source library for reference and reproduction purposes.
Computing Resources. We trained 140,000 models for evaluations (including over 35,000 of gen- erators and over 10,500 for downstream predictors). All our experiments are run single machine from an internal cluster with a GPU Nvidia Quadro RTX 8000 with 48GB memory and an Intel(R) Xeon(R) Gold 5218 CPU with 16 cores (at 2.30GHz). The operating system Ubuntu 20.4.4 LTS.
19

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B.5 TabEBM open-source library
We implemented TabEBM as an extensible library, and the code is available on For practitioners, offers an easy-to-use, domain-agnostic tool that requires no training, making it particularly suitable for data augmen- tation, especially in small datasets. For researchers, the library includes the complete implementation of TabEBM. facilitating future extensions and investigations into class-specific energy-based models.
https://gi htta///andreimaaglloooaaaaaaaei
The library has two core functionalities:
Generate synthetic data: The library can generate data for augmentation.
from tabebm. TabEBM import TabEBM
tabebm = TabEBM
augmented data tabebm. rabebm.generate generate (X_train, y_train, num_samlees=10)
% augmented_data [ctasclass___ numpy adarrad of generated data for a specific "class_id**
%
2. Compute and visualise the energy function: The library allows computation of TabEBM's energy function and the unnormalised data density. The demo notebook. TabEBM_aphe appr_ owwomteddd... sededdtttt.... ipynb, shows the TabEBMMinferred densities under con- ditions of data noise and class imbalance (thus recreating the plots from Appendix C).
B.6 Implementation of Generators
TabEBM. In all our experiments, the surrogate binary classifier in TabEBM is pretrained in-context model, TabPFN [33]. using the official model weights released by the authors (https://githhub com/ /tt/////aaa//////a/////////////t http://minnaaaat///mdee/ee/
prior_diff ceaff_reel_checteee www.eecchecppiintnn.O.. -_ppstthh______p______ cpkt). We use TabPFN with three ensembles. We use four surrogate negative samples, X positioned at aig = 5 standard deviations from zero, in random corners of hypercube in R." (as explained in Section 2.2), distant from any real data. In Appendix D.1, we show that TabEBM robust the distribution of the negative samples.
We use SGLD [84] for sampling from TabEBM, where the starting points x. 2ymth are initialised by adding Gaussian noise with zero mean and standard deviation Jstun 0.01 to a randomly
selected sample of the specific class, i.e., x ~ ~((,, T)
I). For SGLD, we used the following
parameters: step size dsuup = 0.1, noise scale Onoise = 0.01 and number of steps T 200. We found TabEBM to be robust to the SGLD settings (see Appendix D.2).
TabPFGen. We re-implemented TabPFGen [48] by closely following the original paper since no official implementation is available. As recommended in [48], the starting points are initialised by adding Gaussian noise with zero mean and standard deviation of 0.01 to the training points.
SMOTE. We use the source implementation of SMOTE from Imbalanced-leam [45], and the number neighbours k within the range of 3,,3,5, 5). When applicable, we always the maximum value for nearest neighbours (i.e., k = 5). However, very low-sample-size datasets may not contain sufficient samples for large kt For instance, the "fourier" dataset (Nreal 20) only has two samples per class. We set A = 1 to generate synthetic data with SMOTE in these cases.
For the other six benchmark generators, Following prior studies [87, 80, 71, 48], we use the default settings for generators.
their open-source implementations in Synthcity [67].
B.7 Implementation of Downstream Predictors
We implemented TabPFN with its official implementation [33] and the other five downstream predictors with the scikit-learn library [65]. Following prior studies [80, 71], we use the default settings for all downstream predictors.
20

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C Limitations of Existing Generative Methods
We showcase three limitations of current generative models: (1) Appendix C shows that models approximating the joint distribution p(x, y) may fail to preserve the stratification of the real data and even fail to generate samples from specific classes. (2) Appendix C evaluates the approximated class-conditional distributions p(x y) on data with increasing noise levels, and (3) Appendix C evaluates the approximated class-conditional distributions p(x y) on data with increasing class imbalance.
Real
TVAE
20
Class Distribution (%)
10.
5
9
10
12 Class
13
15
16
17
19
20
21
23
Figure 10: Comparison of class distribution between real data and synthetic data from TVAE. We first train TVAE on the cenergy-efficiency" dataset and then randomly generate 10,000 samples with We highlight the classes where no synthetic samples are generated. TVAE fails to generate samples for 4 of 23 classes, showing the impracticability to preserve stratification by generative methods that learn joint distribution p(x, y).
21

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Real data
TabPrGen infereed pixlym0)
TabfffGen infered pixlym1)
TubFli (ours) inferte pixlymo)
TabifiM (ours) inferred pódlymi)
(a) Noise level 0.1 pixlym1)
TabfFGan piely=0)
infered pixly=0)
pixly=i)
(b) Noise level 0.25
Real data
Tab/iFGen infered pldly=))
Tab infereed pixly=1)
TabEBW (ours) infered pixlym0)
TabEBM (ours) inferted pótly=i)
(c) Noise level 0.5 Gam inferted pialy=1)
Real data
Tabiiiien inferee pixly=0)
TabeBM (ours) inferee pixly=o)
TabeBM (ours) infereed piclymi)
(d) Noise level
Real data
TabPFGen inforred pixly=0)
TabFFGen infered pixly=1)
Takeвw (ourst inferred pixly-0)
TakEBM (ours) inferred polly=))
(c) Noise level 2
Figure 11: Evaluating the approximated class-conditional distributions on data with increasing noise levels. Darker blue indicates a higher assigned probability. TabPFGen based model to infer the class-conditional distribution p(x y). As noise increases, TabPFGen's probability assignments vary significantly and end up assigning very high probabilities that are far from the real data. For instance, the areas of assigned probability for p(xly 1) completely flip when noise increases from 0.5 to In contrast, our TabEBM uses class-specific energy models. resulting in robust inferred conditionals. TabEBM performs well even under very high noise (see p(xly = 0) for noise level 2), while TabPFGen struggles.
single shared energy-
22

---

Real data
Tab infered p(dly=0)
Tab/FGen infered pixlym1)
TabEBN (oursi inferee pixlymo)
TakEBM (ours) inferre pótly=i)
(a) Class ratio 150:150
Real
TabPiGen pixly-0)
TabffGen interned
ThBEGN Inferred
TaBEBM (ours) inferred
Class ratio 50:250 TabfFGen pizly=1)
TalfFGGn pixly=0)
infered pixly=o)
TakEBM
Class ratio 25:275
pixlys0)
pixly=])
pixly=d) (ours) pixty
(d) Class ratio 10:290
Figure 12: Evaluating the approximated class-conditional distributions toy dataset of 300 samples with varying class imbalances. The two clusters maintain their positions. Darker blue indicates higher assigned probability. TabPFGen uses single shared energy-based model to infer the class-conditionss distribution p(xly). As class imbalance increases, TabPFGen starts assigning high probability in areas far from the real data, for instance, in the case of p(xly 1) for class ratio 10:290. In contrast, our TabEBM fits class-specific energy models only on the class-wise data x= = (x y c). This results in very robust inferred conditional distributions even under heavy remains relatively constant).
class imbalance (c.g., see that p( p(xly
23

---

D Extended Experimental Results
D.1 Ablations on the distribution of the surrogate negative samples
D.1.1 Ablations on placing the negative samples
hryourcbbe corners lsbeled "negative zamples"
labeeM with sumplees "neeaatvve samples"
with real samples labeled "negative
Resl
8
80
e
negative samples 2
negative samples 22
regotivv somples X2"
Figure 13: TabEBM energy Fa(ar) for different choices of negative samples. The blue region represents low energy, indicating high data density. In (A), TabEBM, with the proposed negative samples placed in hypercube far from the data, infers accurate energy surface, resulting in generated data close to the real points. In (B), labelling a random subset the real data as negative samples leads completely inaccurate energy surface. (C), labelling half of the real points as negative samples reduces density near the decision boundary, as TabPFN assigns low maximal logit due to the high uncertainty. In conclusion, placing negative samples far from the real data results in robust energy surface.
Appendix D. shows TabEBM's ' energy (x( when varying the selection the negative samples. TabEBM infers accurate energy surface with distant negative samples, and the energy surface becomes inaccurate when negative samples resemble real samples. This occurs because TabPFN is uncertain when points of different classes close, affecting its logits magnitude and making them unsuitable for density estimation.
D.1.2 Varying the number of negative samples
We evaluate the impact of the ratio |A [xx]] between the negative samples 2 and the real sam- ples [Ke]. We vary | while keeping [/]] fixed, simulating both balanced and highly imbalanced scenarios. The negative samples Section 2), at five standard deviations in each direction (i.e., O 5). To ensure reliable outcomes, we maintained consistent ratio across all classes, keeping the same proportion negative samples for each class.
placed in random corners of the hypercube (as described in neg
Table shows the results across six datasets with Nical 100 real samples, demonstrating that TabEBM robust to imbalances in the surrogate binary tasks. The column with | = 4 represents the TabEBM results from the main paper, where four negative samples were placed in the corners (as described in Section 2). There are negligible differences in performance, and TabEBM consistently outperforms both the baseline and other generators (as shown in Table 1).
24

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Table 4: Evaluating the impact of varying the ratio | [. We show the test classification accuracy performance (%) of TabEBM on data augmentation averaged over six datasets and ten repeats. TabEBM shows consistent performance and outperforms the baseline, regardless of the number of negative samples.
Baseline (Real data)
TabEBM
Ratio
A : [K
0.1
0.2
0.5
Fixed [.ce
biodeg
76.59
76.54
76,47
76.81
76.45
76.69 +2.70
steel stock
47.16
92.60+7.15
92.7947.50
92.63+7.5
92.71
86.87
90.4643349
+3,6
90,52
90.31
90.36
83.07
energy
31.20
31.20
30.8945.81
30,904609
31.24
25.94
collins 13.064288
13,02
13,05
12.97
13.07 #2.51
11.44
texture
85.9 16.92
85.91 4602
85.94
86,264672
86.01 17:36
82.42
Average accuracy
64.99
64.95
64.94
64.98
64.97
62.07
D.1.3
Varying the distance of the negative samples
We assess the effect of varying the distance of negative samples. We use TabEBM with four negative samples positioned randomly at the corners of the hypercube, outlined in Section (this corresponds neg
to the experimental setup from the main paper). The distance of the negative samples, denoted as dist varied. Table 5 demonstrates that TabEBM remains generally robust to changes this distance, with only small performance variations across different datasets. Importantly, using TabEBM for data augmentation consistently improves performance by approximately 3% compared to the Baseline, regardless of the distance used.
Table 5: Evaluating the impact of varying the distance of the negative samples dist across various datasets. We show the test classification accuracy performance (%) of TabEBB on data augmentation averaged over six datasets and ten repeats. TabEBM is robust, and optional tuning the negative samples could slightly improve performance.
Basclinc
TabEBM
(Real data)
Per-dimension distance og the negative samples
0.2
biodeg
76.72. 76.72.333
76.62_..40
77. 77.12:2200
76.85
76.504395
76.45
76. 76.6912.0
steel
93.97.5376
93.46-6.24
93.00=6.92
92.60
92. 22.68
92.71
86 87
stock
90.42+346
90.29
90.56
90.38+364
90.43
90.364314
89.07
energy
31.73
31.42_6.08
31.864x112
32.53
31.654605
31 31.244555
25.944486
collins
13.0342259
12.92-240
12,97
13.03
13.084293
13.07
11 11.4442m
texture
85.62+741
85.58=1.49
85,50=7.65
85.05
85. 85.20+795
86.01
82.42+1038
Average accuracy
65.25
65.05
65.17
65.07
64.92
64.97
62.07
D.2 Ablations on the sensitivity to the hyperparameters of SGLD sampling
We vary two key hyperparameters
SGLD on the "biodeg" binary dataset with NNeal = 100: the step size assepp and the noise scale Qgeise- Table 6 shows that TabEBM remains stable with respect to these hyperparameters. Note that smaller values of anoise are expected to perform better because SGLD sampling adds noise each iteration (see Line 7 in Algorithm 1), thus larger values of Quoise will hinder convergence of the SGLD sampler.
25

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Table 6: Test classification accuracy (%) of TabEBM (averaged over six downstream predictors)
with different SGLD settings. Increasing moise (added at each SGLD step) is expected to degrade performance, as causes the sampling to diverge further from the real data.
Onoise
Ostep
0.1
0.3
0.5
1.0
0.01
76.45
77.09
77.04
76.58
0.02
76.86
76.96
76.77
76.26
0.05
75.93
75.89
75.94
75.70
D.3
Distribution of Logits and Unnormalized Density in TabEBM
15.0
blodeg
15.0
fourler
15.0
steel
15.0
protein
Logit value
7.5
7.5-
7.3-
3.0
3.0-
5.0
3.5-
2.5
2.5
2.5
Loght (x000) for
2.5
Logh
0.0
0.0
0.0
Distance
Distance from the fourler
Distance
Distance the real data
Unveomm. dunaity b41000)
500
blodeg
Unnorm, density 022000)
Unnnamm dunaity (x1000)
steel
Inmorrm density (x1000)
protein
400
125-
200-
300
100-
1.00
80-
75
60-
50
1000
20-
10
20
35
20 Distance from the real data
30
20
10 20
Distance from the real data
Distance from the real data
Distance from the real data
Figure 14: Additional results for Section 3.4. The logit distribution of TabPEN trained on our surrogate binary tasks across four datasets. Starting from the real samples, random points are selected increasing distances (shown on the x-axis). The top row shows the logit distributions for the surrogate task. Close to the real data, TabPFN outputs a high logit value. As the distance increases, the logits converge due increased predictive uncertainty, leading equal class probabilities after applying softmax. Notably, across datasets, TabPFN's logits are always positive, have similar ranges, and maintain relatively constant sum as distance increases. The bottom row TabEBM's unnormalized density, pr( & density decreases significantly far from the data, becoming negligible. Because sampling using SGLD perform gradient ascent the density, the BabEBM-generatte samples will be similar when using one or both logits.
- Pe(x)) x (ex)(f(=)[0)) + exp(f(x)(1))) The
26

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D.4 Complete Trade-off Figures with Error Bars
Normalised accuracy improvement (%
10
10
TabEBM (Ours)
TabEBM (Ours)
TabPFGen SMOTE
TabPFGen
SMOTE
-10
-10
TTbDDPM GOGGLE
TabDDPM
TVAE
TVAE
CTGAN NFLOW
ARE
GOGGLE
CIGAN
RF
20
20
NFLOW
0.0
0.2
0.4 0.6 0.8 1.0
0.6
0.7
0.8 0.9
1.0
(al) Inverse KL (train, syn) 1
(a2) KS test (train, syn)
10
10
Normalised accuracy change (%)
TabEBM (Ours)
TabEBM (Ours)
SMOTE
SMOTE TabPFGen
JabPFGen
-20
TVAE
ARF
-20
ARVAE
CTGAN
OTGAN TaRDDPM NFLOW GOGGLE
Tab IDDDDPM
NFLOW
GOGGLE
-40
-40
0.2
0.3
0.4
0.5
0.5 0.0 0.5 1.0 1.5 2.0
(b1) DCR (train, syn) t
(b2) 8 3-presence (train, syn) 1
Figure &al)))): Median inverse KI. and KS test vs. mean normalised balanced accuracy improvement (%) between real train data and synthetic data. (b1&b2): Median DCR and 5 presence vs. mean normalised balanced accuracy change (%) between real train data and synthetic data. Note that "accuracy improvement" is for data augmentation, and "accuracy change" is for data sharing. TabEBM generates high-fidelity synthetic data that can also be used privacy preservation.
27

---

D.5 Results on Data Augmentation
D.5.1 Results on eight OpenML datasets.
Table 7: Classification accuracy (%) of LR, comparing data augmentation eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datascts. A higher rank implies higher accuracy. Note that "N/A" denotes that specific generator was not applicable or the downstream predictor failed to converge, and the rank is computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample sizes. TabEBM achieves the best overall performance against Baseline
and benchmark generators.
Baseline (Real data)
Dutasets
Nuat
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabEBM
04
N/A
22
21704g476
18:40gam
18.77
25 22
36.61
38.01 27.38
50
62. 14
61.49
37,042229
33.10 18.10
31.25
23.98
43.64_1m
54.95-325
63.000-0
63,022384
100
79. 34
79,53
61.07
55:44219
46.3744.0
45.55-424
56.77=306
67.25+45)
-0.54
80
42
200
31.53
90.92213:
47.43
71.27
66 1644n
66.372322
70.52-21
76.30-37
-1.69-1m
21.7
500
97.86
97.69
90.77am0
89.05
85.09
83.58
88. 18.55
90.61
97.97
97.88
20 42.90
N/A
22.46+5.8
16.00=410
15.484399
13.58
15,80 22.04-443
44.67
43.02
50
60.62
58.40.1.5
33.42
31.18
28. 2374
26.18
39 39.04:20
20.00
60.07
60.36
67.76.249
65.84-233
41.36x2.55
40.32:344
40.32
41.44=50c
47.90
39.78
67.40-1.51
67.444244
most 10 clatses
200
73.13 1::11
71.56 1247
14.76
55.00 112
58.08 1.5c
58.48 110
50.98 1244
70.30 1.:9
72.38 17:0
500
77.44
21
68.28
28:18:139
68. 121122
72.36:146
71.54_118
19.48
76.52:330
77.5 77.50.3.1e
20
71.34
70.10
10.16
58.
58.05
49, 49.99
62.61
69.47
71 71.24,400 70.76.330
76.35 a
75.69 ueen
23
62.87
49.44
71.75 -4
75.68_.
76.41
bindeg
100
78.91 2
78.39
77.09=2.0
74 2254
68.62+53
55.61 23,5
75.
77.92 72.45
78. 34 24
200
82.00
81.42
80.07
78 28.56
72.35
59. 49.06_246
78.03
81 81.24_100 73.73
81 2
500
K3.74
a1.69
78 23
77.98+122
2000
57. 2378
60.27
27.9
53, 10
54.20 24.20
55.41
53. 23.2
66.81 29.74
67.03
50
87.91
1:
69.01 20
66.22
66.22 22:311
57.05+531
57 47.46-44
64.81
57.20 $7.20
90.63 90.63-475
92. 20
stoo]
100
98.5
85
82.67
24,33
70.49
65 65.09
52.77.2100
67.85
61.62
99.24
99.21
200
17 20.35
#2.77
70.4423377
11.9
20
64.52:211
99.51 =000
500
99.75 10:3
96.63 1:::
94.59 1230
96.32
14
98.07
95.35 200
10.1
99.8 84 g..0
99.8 1,000
20
77.99
80.15 Loss
74.21 ja:
59.20 12:00
12.50
72.09
69.04 .a25
80.59
79.54
80.39
stock
82.1 21
08
81.49
76.41
79.85
78.47
72.95=217
25.4
78.44.440
80.82
76.91
75.49:331
17.65
82.37
82.37
82.21
11
200
82. 103
84.29
11.33
29.24
29.86.112
11.4
80.21 2213
78.87 3.46
76.91.104
83.75
84. 174.17.142 $1.2
than e0relazses
50
22.22
N/A 10.11
9.58
7,70
8:20-
10:51-125
17.10g503
NIA
2.1 16.66-
energy
13.80
13.0
14.14
10.79
15.652240
28.10
200
N/A
16.39
16.56
16.78
18.11
20.10-244
20.922223
collins
200
100
14.28
21
19.39
N/A
10.57
16.03
11.61216
10.97a146
9.59
13.31
17.06-131
11.31
K.60
17.80
12.184133
NIA
NIA
1953
14.01 +1.55
86.56
86.93222
55.01
41.634541
60.074mm
11,6--50
77.68-433
58.54:188
100
07
23
65,36
60.07:311
60.76
73.16.211
64.69_411
84.13
NIA
94.38 1124
texture
200
96.65
96.53-1.33
75.91
80.02.1:13
77.07
86,2 86.24=1/2
85.9 85.90-13
85.94
NIA
96 53 53
500
98.03
98.05.013
91.87
92.93
90.0
91,83 93.
91.72
NIA
97.75 ab42
Averuge rank
2:3
3:35
g.45
p.08
7.61 733
6.70
1,92
28

---

Table 8: Classification accuracy (%) of KNN, comparing data augmentation on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets.
higher rank implies higher accuracy. Note that "N/A" not applicable or the downstream predictor failed to converge.
denotes that specific generator and the rank is computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample sizes. TabEBM achieves the best overall performance
against Baseline and benchmark generators.
Datasets
Naa
(Real data)
SMOTE
TVAE
CTGAN
NELOW
TENDDPM
GOGGLE
TahPPiGeen
TabEBM
20
21 34
NIA
21. 21.78
21.18
21.30
22.00.210
22.69
16.99
35,78
35.76
50
36.41
55.24
35.85
36.13
35.40
34177
36.84
53.38
53.49 1370
protein
-0.17-a
20.11
51.97
50.614315
50.624327
50.63
50.36.244
44.70
67.99-243
68.27
200
84 m
80.43
65.52
66.05
66.14.2.
67.50
66.52
79.94 63.92g5
m.
80.55 gm:00
500
85 2146
90.92-142
87.08
88.77+14
85.51
86.47
85.87418
85.642134
91. 91.32_110
91.67=1.11
18.00
N/A
26. 52252
24.88
19.80
19:30ga3
23.422344
18.784212
41.08
42.78
00
60.38
39. 83
46.822332
43.56
19.54
42.9
12.98:2.
28.124225
19.50_1.9 59
54
fourierr
100
5% 36
66.96_247
48. 441444
53.945347
53.50.13.4
60.00:411
52,742513
35.70s244
63 28588-25
65.08
65.08:147
classes
200
60-
71.90=200
59.66s331
66.512215
65. 65.1642.
70.22
61.522224
51,24
70.32-1144
71508=187
500
27.64g1um
13.20
76.22
75.72
78888
76.54
63.66.2.w
74.30...51
20
23 m
68.99 1131
66.63
16.99
59.91 150
55.85
58.77
56.6227.2
67.77 67.79-444
69.76.
50
71.26
73 2.
70.50
70.00
65.90
70.23
65,29
72.08
73.58
biodeg
100
76.
76.07
14.02
1233
73.24
77.34
12.26 12.28
74.56
200
$6_66.
188 83.07
27.31
77.64
27
78.8 22
76.82
77 77.46_114 68
500
82.50 59
82. 13
82.17
82.80
81.06g1
82.15
82. 32.10
79.99
81.01 1/6
20
56 44
63.95
59. 45
57.04
24.5925.1
65.462510
56.97.5.4
$2.9045.5
70.68
69.
73.95_47
70.24 20.24
67. 10
68.774245
67 67.00
85.14
64.022:71
57.54:234
20
stool
100
70
27746
71. 71.87
72.94
77.09220
94.05.114
72.62
08,08 28.
87.77 2.11
87 4322
200
90.44-200
82 82.46=145
80.83
82,73
85 85.49.3.9
98.99
83.38
69. 69.12s235
92.01
92. 92.06=144
500
94,99
89.97
91.34
12.42
93.37
99.71,021
12.02
19.79.197
95.08
95.50
1s 89.77
13.80
68.93 mo
81.82
6
1116
stock
100
50
89.66
33
03
92.32
1.0
89.58
84.32
19.61
83.49
$9.66
84.43
91.40
29.34
84.33
89.6613
59.44.mm
83.64:253
92.02
89.67
92.47
89 1277
200
91.65
06
23446-043
92
91.55
91.43
92.92.100 ce
91.14
91.53gr0
93.15
93.62
10 closves
70
N/A
10:64
8,22
883
8924251
9.14
11866233
2.2
energy
100
18. 213
N/A
13 13.71
1588
14.67
16 18
15.71
17.64-208
NIA
29.82 1.77
200
26.45 45
N/A
20.71
21.71432
23.40
23.95
23.094236
27.35 27.35+228
NIA
35.93 2539
collins
40.59-144
NIA
7.58
7.95
2.55
14.24
7.42aum7
8.79
15.16
200
15.84_1174
19.81
9.79
11.21
12.24
16.30g1.4
10.96
12.86
NIA
13.05 116
50
16.96... 2440
78.80 2.75
55.5
61.86
62.08
61.91
62.67
,698
NIA
75.57
100
77.16_111
86.15
69.54
76.53
76.85
77.77
76.70
72.64.181
NIA
84, 83
g1
15.4
14.62
1139
65.11
p4.72
89.45
13m
500
91.40
93.14
29.88
91,40
91.34g1m
92.31
91.46g151
91.91
NIA
93,46
Average rank
0.
2.70
7.67
7.03
7.27
4.12g234
6.82
8:4222
3,67
2.15
29

---

Table 9: Classification accuracy (%) of MLP, comparing data augmentation eight real-world tabular datasets with varied real data availability. We report the mean = std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes that a specific generator was not applicable or the downstream predictor failed to converge, and the rank computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample sizes. TabEBM achieves the best overall performance against Baseline and benchmark generators.
Datasets
Baseline (Real data)
SMOTE
TVAE
CIGAN
NHLOW
TabDDMM
GOGGLE
TabPHGien
TabEBM
20
35.12
NIA 21
g6.95
24.56_50
27.96
27
36.19
36.26.2.6
50
14.11
57.24
40,77:14
4304g50
44.78:1m
49.43
46.8415t
44, 44.78
58.62
58.75
protein
100
76.82
76.782210
22
64.142219
63.242416
69.202225
68.08226)
62.45
77 27.6323.0 77.84
200
89.53+224
90.28-2115
80.38
81.94
85:48:201
82.57
78.04
90.74.213
90 90.48 210
500
98.23
98.25
95.08
95.74
96. 16.1e
96.01
96.50
96.23
98.52
98.50 =8.50
20
33.66
NIA
Ls
17.08
1m
18.32
23
19
37,00 1:
35.02 17
11.7
g3.02
37.16
37.60
14:44
40.90
42.82
32.66
12:3
2:440
fourier
100
62.78 11
61.44g374
43.68 is
48.
46.
18
56.52
52.50
63.00 21 95
63.54 1165
mout clooses
2001
70.06:2210
58 56.9002236
62.36 26
58. 18.40=253
70.185150
62.144200
+1.49 50.9223:1
71.
77.94
77.18 35
72. 74
74.30 m6
11.382154
77.782126
74.3221.5
67.28
78.34
79.30 20:00
20
71.31
68.84
66 66.64:.22
62.6 c2m
52.96
62.06
65.81 2224
22.04
72.09 -481
50
76.73
74.97 =251
72.022474
71.83-111
67 M0
69,922443
74.005:31
71.01 2273
77.17+299
77. =3:00
biodkg
100
79.13
18.20
76.78
77.85
76.01
76.74
76.08
76.24
78.23
79.06
2:.43
81.70 21
20.43
79.96.235
59.92
80.5
80.34.199
21.74 36
82.24
500
$4.50 1m
84.50 Lost
83.78
83.67 Lost
84.13 g4
84.09
83.76
82,97
84.37 in
84.14
20
62. 36,3
60.3 00:34.575
61
1
56 11
60.67.4
55.23333
55, 55,78.3m
64.49
64
26
45.68
18
69.01224
70.30g4m
66.96_112
84.04
64.79240
58.95
82.72
82,
stool
100
92. 28:3
78.44 2357
76. 16.37
76.92
76. 76.50-11
95.83
71:85;
67.35
16.11
95 1:225
200
97.3 37.31::
83.93
82.42=275
81.70=254
84.06-444
98.75
79 18.66::15
78.36
98. 18.83
98.84 =0:67
500
99.78
91.37
93.08.112
43.99.11
99.47.041
90.34;211
96.06.110
99.81
99.8]
p3.5
77.25 g406
69:90
72.8 7m
80.00
69.30
83.34
1:000
30
40.57
89.71 g1
6262211
79.35
81.52
88.48
83.36 30
88.38 88.38
90.23
90.38 2017
stock
100)
90.63
91.17
88. 37
83 19
90.65
88.64 68.64
91. 91.61
91.700
21.70.1.7
91.75
91.25
22.58
91.27
90.34
89.32
92.19
90.37
91.89
20
10 cinsses
50
24.79.1.7
NIA
12.51
12.61
8m
10.91
12.45
20.42
NIA
24.04 1:300
energy
100
21
NIA
16. 1
g5
15.70
17.75
18.16
20.72
NIA
29 30
2001
1243
N/A
22.30.244
23.00,411
23.5
26.12
26.28111
$3.03
N/A
41.27 1330
collins
200
14.16
19.35
19.06 49
14.622200
9.24
13.17
9.162.st
12.38
2.04
18.632155
14003
12.48
8:59
10.81
17.65
N/A
N/A
19.53
14.07 1:58
50
$4.50
84.12
62.92.410
67.69.1.0
61.99
69.69
64.45,7M4
29.68
N/A
85.51
Texture
200
93.81
91,50+1.4
14
91.57e129
74.53
86.57
79.96-437
90.68
88.97 2:12
80.36-454
85.42e214
90.10
80.23+211
19.14
91.661140
65.59
NIA
94.35
=151
11:57
500
46.55
20
94.66
96.27
94.34_136
94,72gnsi
95
26.49
NIA
97.13
Average
3.00
4.06
7.82
7.48 so
8:45
5.
7.48
6.82223
2.67 19
1.67
30

---

Table 10: Classification accuracy (%) of RF, comparing data augmentation eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes that specific generator was not applicable or the downstream predictor failed to converge, and the rank computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample sizes. TabEBM achieves the best overall performance against Baseline and benchmark generators.
Datasets
Baseline (Real data)
SMOTE
TYAE
CIGAN
TabDDMM
GOGGLE
TabPPGien
TabEBM
20
NiA
22
24.94
24.61
29.62
27.69.1
25.76
22.04
34.19 23.0
50
55.691761
46.95_11
43.91
43.28_1m
47.93
44.48
47:25
54. 54.291397
56.85 13.0
protein
68.19
72.89
63.24-177
61.192210
49.642344
68.192411
60.05
65.05_110
71.47
72.57=1.0
200
80.34
80.34
60
78.51=258
75.84
78.74.224
75.61
79.44-211
83.36,224
84.30 11.07
500
93.01
93.82
92.86
91.77:us
93.00
92.93
92.38
92.95
24.49
93.91
20
35.
NIA
19:06
17.52
20.78
16.98
13.78
19.00
34,88
38.60
24176
37.20
34.82
17.78
51.76
44.22
53.86
66.92
fourier
100
g3.86
73.78 g3
64.40
60.82
$1.64_116
66.1421s1
58.62g1
68.
73.13
74.84:
mout clooses
2001
79.18 75.54
74 74.862100
74.26
69. M6ste
76.422155
12.88
76.64
82.20
79. 18
21.84
81.02:1 59
81.18::41
80.08
81.26
80.28
80.62
81.45
83.40=122
20
61.1
27.7
68.38 1550
65.44:.10
56 26.0
52,90
62.33
63.52,n21
67.82 15.15
50
68.
38 44.52
70.64
71.77=220
66 78
61. 61.39
63.98218
6M.7843:1
70.3442139
71. 71.38
72.12
biodeg
100
73.19
75.36_156
74,96
72.68
73.11
72.16129
74.22
75.85
75.65
78.86 97 22
76.42-2
76.68.2m
13.43_am
76.162200
15.79
77.42-234
21
79.22
500
$1.42,om7
82.03 g:
B1.88
81.71
81.43
81.34.1 1
81.94
82.38
82. 22.10_113
20 52,77
56, 16
37.23
24.65
13.75
51,70gres
54.00
55.50
57.04,330
57.41
59.7843.1
12
28.09
58.14
57.674252
60.34-250
43.07
67.74_)55
stool
100
64.97
69.08...2
64.46
61
60.53
62.71:34
63.07-211
73.28
79.63 -3.4
200
25.45
74.71 2339
71.45=211
68.
68.52e130
62. 15=230
68.10
67.61a13:
67.36
85.12
88.85 =1.10
500
90.93
85.63,314
:4.51
mm
89.19
81.4120
60,35
11135
95.90
2016
19.471588 15:3
81.99 p.
77.94 1131
12.53
80.09
12757
18.10
13.96
1346
stock
1001
30
91 +1.44
$7.57
91 21.47-215
89.69 e1 se
86.62 62
91. 227
g3
89.82
89. 89.33.1m
24.28
91.33
88.69
84
90.48
88.65 23:5
92.00-211
92.07
89.35
89.99
92.17
23.6
93.52
93.94 0e
93.35g10
92.62
92.77
93.65
93.08
93.87
93.65
10 cinsses
18.96
NIA
16.63
15.66
15.66
:4.81
14:4
15.05
15.58
NIA
27.74 23:71
energy
100
30.85
NIA
24
28.59
28
27.59
27123
17
25.43
N/A
41.03
12.3
N/A
42.10
41.691181
44.41.351
44.58
41.331590
44.64
N/A
53,87
13:1
20.4
6.75
8:23
2.34
12.84
6.73
8.43
N/A
13.35
collins
200
13.75
17.56
10,51
11.00
9.85
13.15
9. 9.90ga
13.40
N/A
16.51 115
50
71.27
71.17
57.41
62.78.421
65. 24.24
69.45
62.93,444
64.33.127
N/A
75.79 cm
80.40+244
80.38
65.63-441
75.38
77.67=2m
79.3
75.98+256
77.30=244
82.30-111
Texture
200
$4.00 11:55
15.
76.98 122
84.44
85. a...
84.00
83.70
80.02 11:00
NIA
85.92 1.15
500
89 89.4
90.17
88.97
90.00
19.99_10
90.17
91.01
88.98
NIA
90.77
Average
4.364135
3.02 14
25
7.82
8.45
6.12g03
7.85pmm
6,00 35
3.12
1.38 29.7
31

---

Table 1I: Classification accuracy (%) of XGBoost, comparing data augmentation on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes that specific generator was not applicable or the downstream predictor failed converge, and the rank is computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample sizes. TabEBM achieves the best overall performance
against Bascline and benchmark generators.
Dainsets
New
Raseline (Real data)
SMOTE
TVAE
CTGAN
NELOW
TabDDPM
ARF
GOGGLE
TabPPGen
TabEBM
20
6337
N/A
19:44
175
18.11
16.15_138
20.71
17:40
24.18 24
50
39.01
37.68
33.07
24.38
23.09
30.87-370
34.13
33.62:36
39. 39.78
44.46:497
protein
57.59
60.16
49:23
43.33
37.69
48.36-448
43.97
53.74 47,00-129
62.77 4553
200
21.
76.90_4xe
69.71
67.46-439 39
58 29
69.68-421
63.69
66.09-441
73, 19
79.25
500
88.
89.9
90.02-1:5
90. 20
86.03
87.29
90.05 20:0
K5.04-20
89 19.662117
91.81
20 10.00
N/A
14.64
13.58
13.82.s.1
11.72
16.38
12.34_159
23. 23.50
26.78
50
42.10
33
14.32
24.68
17.66
14.82
27.74
35.42
35 :51
45.08
24.81.277
52.92.5ta
15
30.36
42,46_.1
40.28
43.
54.94 1877
Acmost 10 clazses
200
63.88
1:3
65.34
58. 13.77
53.20 525
46 14.5
61,40_.112
10
$6.66
66 64,60
67.68 1311
500
74.56
74.18
68. 28.5
67 67.98
61
72.78
67.3
47:50
68.28
N/A
76.25 76.25
20 62.95_140
65.51_551
62. m2
15
59 20
54.65_154
62.
65 65,52
66.64
:0
67.96_144
67.69_10
61.64_671
60,72,475
$7.48
69.4
66.97_14
67 76
biodeg
73.88 2.54
72.05 (475
72.11 12.11
70.4
1a2s
71.1
69.03
12.58
1570
200
2433
14.98
a3.93
75.68
67 67.82
72.58
74.74a22
13.84-1122
75 g5.85
76.74.24
500
28.4
19.3
78.88
$0.15
76.72
77.10:116
78.14
-8.83-111
79.40s1.0
78.50
20 53.12
55.64_435
55, 36
52, 38.3
52,44_114
51.34
50.74-113
25.45
55.78
50
66.73_s.11
60.79
59.51 2415
22
54. 84.79
59.71=a54
57.66450
55,89
63 78
74.18
83.17 16
66.95_.51
61.72gxa0
65.12
60.56
12.02-1144
59.67
59.04-11 is
90.52gn47
96.55 2266
200
95.94 mm
81.21_55
70.64_
70.26
74.50.3119
74.57
65.41
99.14 19.14
99.54 1007
500
99.95
97.01_234
95.27
89.46_sss
83.25 15:10
91.72,1534
87 87.59
1535
100.00.nan
100.00
20
78.92=311 76.42
67.46=15
60.56_9.
23.36
77.45-110
69.15
70.88-132
79 c9.82
83.44
stock
100
83.71 1:00
88.
89.00 20:00
26.23_225
84.65
79.31
84.60 27
76.27
82.50
W007214
85.70
81.6
26.09
84.98
34.67_23
87 28
66
200
92.32 1:35
92.26..33
90.94.1
89.01 89.012251
88.92
91.36_174
91 91.04
91,42_334
91. 91.72
92. 11
.0
12.05
N/A
11:60
14,47
10.95
10.21
12.8
12.34_
N/A
21.07
100
29.37
NIA
20.61 1530
19.81
22.71
22.27
12.02
10.01
N/A
27.93
44.96_3311
N/A
33.7
35.92_545
33.71
34.73
37.06
18.81
45595
collins
200
100
10.58
7.77
2357
11,46 1
N/A
7,76
9:43
6.52 16
9.84 56
6.10
8.26g175
89
9:00
6.21gr
8 8.00gnss
5.96.11
9.79
N/A
N/A
11.72g1 91
More
50
16
60.99 10199_115
45.76
39.50
43.02
s0.22
43.71
46.21
N/A
69.11
100
68.96,344
69.77_16
51.95 1ow
S5.52_734
63.23
65.59_112
17.01
62.06_s11
N/A
76.35 1264
77.91
1.5
81.55 .332
70.70
71.60
73.76,5m
17,66.11
72.56
2215
500
89.37 2111
89.87
26.2.
26.80
86.83
86.52.1
85 25.70
87:07
N/A
29.6
Average rank
3.64
3.45
6. 6.32
7.33-2m
8.64.1.2
6.30
6.4.22
7.62.114
2.44
1.2.121
32

---

Table 12: Classification accuracy (%) of TabPFN, comparing data augmentation on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. denotes that specific generator was not applicable or the downstream predictor failed converge, and the rank is computed with the mean balanced accuracy of other methods. We bold the highest accuracy for each dataset of different sample sizes. TabEBM achieves the best overall performance
higher rank implies higher accuracy. Note that "N/A"
against Baseline and benchmark generators.
Baseline (Roal data)
Datnsets
Nedi
SMOTE
TVAE
CTGAN
NELOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabRBM
20
27.
N/A
19.21
20.58-244
20.80
18.89
23 23.97
10.55
33.42_599
44.634500
55.24 24.
59.85_135
43.58
37.374401
34.42
21.70gn44
46.02,250
13.54
57.63-29:
58.88
protein
100
20.05_1166
68.15
71.10
57.89
59.28
84gas
23.6921044
77.60_409
28.26
200
89. 18.67.1
91.79 1:
87.05
N6. 13.8
k3.29
87.39
85 4
77.65441
90.77
90.94:
500
97.31
97.69
47.5
97.584405
96. 4002
97.44
97 40,40
97. 97.35
97.24-0
97.28
30.06
NIA
22.00
20.10
14.52
12.22
64
N/A
36.56
1476
53.08_1144
45.82:422
37.46.550
28.78
22.74
14
g1:30
15.1
fourier
100
64.62 1411
63.66 63.66_190
56.68 16.68
$4.78
44.5
49.36
54.74
21.40
65.95
65.40
Atmont elavees
200
71. 11.62
70.56
66.14 14.4
62.64
12.12
66
52 18
69.93
72.48 15:00
500
77. 21
77.50_
77.82
29.1 21.90
24.36
77 77.30
69.02,137
29.2
58.2 38.28
50:00
51.80
70.68
71.18
75.27 uhwa
74.65 1
23
70.21
55.68 19m
50.00
$5.75
75.69
75.56, 1..66.17
biodag
100
78. 93.9921
77.78
77.27
71.7
63.50
57.50 (.m
11:25
65.87
78. 15.15
79.00
200
82.59
81,42
80.48
80.19
79.16
80.45
g0.58
80.66g140
82
82,58
85.00 pm
$4.37_47
84.40
$4.67
g4.58
83.66
56. 87117
55.95
56.03
35.62.4..0
52.52.444
50.00
2313
50.05
64.30 st
65.87
50
82.34
63.42
62.08 12.0
63.99
$2.92
50.61 1om
61. 61.32
50.36
$1.70
86.30
Moel
100
97.37
73.06-444
71, 71,9612.0
72.23
8087 8087 56.34
69 23300
51.18
97.49
97.81
24.30
82.32-224
81.78
83.2442u
62.92
99.35
$6.40:421
64.4221133
96. 06.80-a13
98.964477
500
99.71 Ln:
91.27 2.50
91.
96.98 11.34
98.32 11:9
99.88 1n1s
95.70
98.56
99.77 a
99.74 202
20
83.18 18
83.69-3.10
74.01=3m
56. 16.92
78, 78.73 74.99
69.61 69.612sss
73.40a411
82.95
83.81
stock
100
90.0
92.099114
90.0112243
90.754:20
82,27
89.43
78.9 78.91
86. 1645es
78. 13.94
92.124116
89 89.68
90.17au::
83 83.72.2m
89.
79. 79.00
39.95
92.122-111
90.15
200
91.16
93.99
93.57=1100
93.28
91.92=2m
94.22
93.05
92.07
91.17
94.16.107
Average rank
2.08
4.23
6.12
6.29
8.42s1.52
6.12
6.51g151
8.53
3.12
2:23
33

---

D.5.2
Results on six UCI Datasets
Table 13: Details of the six real-world tabular datasets from UCL.
Not ovaluated in TabPFN [35]
# Samples class (Min)
Samples per class (Max)
Datasct
LC
Samples (N)
Features (D)
Classes
N/D
clinical
890
2,139
521
1,618
support2
850
9,105
mushroom
auction 713
2,043
abalone
4,153
519
689
statlog 144
1,000
2 50
300
700
Table 14: Test classification accuracy (%) aggregated over six downstream predictors, comparing data augmentation on six leakage-free UCI datasets. Note that "N/A" denotes that a specific generator was not applicable. TabEBM still achieves the best overall performance against benchmark methods.
Datasets
Baseline
SMOTE
TVAE
CTGAN
TabDDPM
TabPFGen
TabEBM (Ours)
(Neat 100)
clinical
68.66 68.63 1581
71.07 1467
61.80_2.6
65.21 1577
54.03
69.66
71.20 13554
support2
64.23 11.99
65.60
60.70 60s0
19.14
38.3111.74
14.14
65.28
mushroom
95.51=228
95.844199
93.75-1.18
93.26-246
79.87=229
97.05+1.56
96.82+1
auction
$1.90
1..3
53.09=a91
52.35
51.14_1.76
56.82 N/A
abalone
11.59
N/A
8,49=122
7.72=267
9,95=24s
13.56
statlog
56.22
57.30
53.1221152
55.55
=3.07=2255
57.65
57.85
D.5.3 Results larger sample sizes
Table 15: Test classification accuracy (%) aggregated over six downstream predictors, comparing data augmentation with increased real data availability of the "texture" dataset. Note that "N/A" denotes that a specific generator was not applicable. On larger datasets, TabEBM still outperforms other generators, but training on real data alone appears sufficient. This highlights TabEBM's usefulness in fields with limited training samples.
Accuracy improvements by TabEBM (%)
Naa
TabDDPM
(Ours)
13.4
76.40+10.30
55.33a620
54.80=12m
62.94
78.90=136
100
82, 123
84. 84.35
66.00
69 m9
76. 24.34
N/A
86.01 1736
+3.50
200
87.54
89.29
78.37
82.44
82.512599
N/A
89.77_sm7
+2.23
500
92.96.407
93.69
90.092356
91.48_1.0
91.24_115
N/A
93.76_364
+0.50
1000
96.37
96.21
93.61 1:300
95.36_171
94.56
N/A
96.30
-0.07
2000
97.76
96.842144
96. 1.2
97.10
97.13
N/A
97.83_1.45
+0.07
3000
98. 28.20
98.28 1o:0
97.60_n77
97.60
97.73 LoV1
N/A
98.35
+0.15
4000
98.51
98.59 10.36
98.11 1440
98.00..20
98.46g004
98.55gass
+0.04
D.6
Results on Statistical Fidelity
We aim to provide fair and coherent comparison between TabEBM and existing methods and thus follow the widely adopted evaluation process in prior studies. Specifically, compute the three statistical fidelity metrics with the open-source implementations from the well-established benchmark, Syntheity. We note that the previous studies [87, 67] often operate under the assumption that the issues associated with multiple comparisons are less pronounced in generating low-dimensional tabular data, hence correction methods for multiple hypothesis testing are seldom employed. Following such assumptions, correction methods are not employed in this work. In addition, we would like to point out the imperfection of widely adopted univariate metries (i.e., Inverse KL, KS test and test) in existing work. However, evaluating generators' ability to capture the joining feature relationships remains an open research question [78]. We leave this for future work explore.
34

---

D.6.1 Similarity between Real Train Data and Synthetic Data
Table 16:
Inverse KL between real train data and synthetic data on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher fidelity, Note that "N/A" denotes that a specific generator was not applicable, and the rank computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. TabEBM achieves the best
overall performance against benchmark generators.
Datasets
Naai
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabEBM
20
N/A
0.1
g.20
0.34
0.07 2000
0.22.200t
0.07
2.46
0.77
50
0.88=001
0.80
0.66:ams
0,87
0.07 #0:00
0.87=2001
0.50+004
0.82:2006
0.94-on2
protein
100
am
0.78
0.90gam
0,07
0.91 :001
0.32
0.92:
0.96-001
200
0.95=mm
0.75
0.83
0,93
0.08
0,93-2001
0.1 4:01
0.94
0.06
500
0.962am
0.70
0.87
2.94
2.09
0.95
0.1 0.13
0.96.2011
0.97
20
N/A
0.12
0.15
0,27
0,50
0.50
0.5 0.50
0.97=20.0
0.87 0.87=001
50
mm93
2.79
0.66gnas
0.90
20.00
0,90=0000
0.47 2:05
0.87-20.2
0.95_001
fourier
100
0.95
0.76
0.81
0,93
0.07
0.94 0.94=2001
0,20
0.94
0.97-001
most 10 elasses
200
0.97.am
0.61
0.82
0,95
0.09 2.09
0.96.0000
0.08
=.97
0.98_0000
500
0.97.a00
0.522003
0.90gam
0.95
0.10
0.97=20.0
0.09
0.98
0.98
20
0.47
0.43
0.43
0,50gaas
0.34
0.51 -0.04
0.37
0.60
0.87
50
0.62=000
0.59
0.56
0.63
0.28 20.02
0.65
0.41 0:00
0.75
0.90 0.90-=0.2
hiodeg
100
0.69
0.66
0.65
2004
0.30
0.69 20,05
0.38
0.76
0.90 0.940_0004
200
0.71 2003
0.65
0.69
0.68
2.29
0.69
=0.00
0.34
0.79
0.91
500
0.80
0.68
0.73
0.75
0.26
0.73
0.81 10004
0.92 0.02
20
0.45
0.37
0.40
0.47
0.07
0.43-2005
20.05
0.53
0.84_000
50
0.70
0.57
0.59
0.64
0.13 10,00
0.63
0,23
0.71 10.00
0.91 0002
steel
100
0.71
0.55
0.63
0.67
0.13
0.66
0. 0.20
0.75
0.92 0.92-0003
200
mm75
0.50gau4
0.65
0.70
0.13
2.67
0.17 0.17 2001
0.77-20.4
0.93__mm
500
0.75
0.5
0.66
g.70
0.14 0.14
0.68
0.19
0.80..006
0.94
20
0.55
0.45
0.43
0.60
g00s
0.24
0.52
0.35
0.68.20.2
0.89
0.92-aao2
0.73
0.78
0.86
0.37 soon
0.88
0.32
0.91 =0.0
0.95-0002
stock
100
0.96
0.67
0.83
0,91
100s
0.49
0,93
0.17
0.95
0.97
200
0.98
0.63
0.80
0.92
0.83
0.95 0.95
0. g.00
0.98
0.98
More thon 10 elasses
50
N/A
0.25
0.34
0.42
0.24
0.49
0.24
N/A
0.80
energy
100
N/A
0,282007
0.42+am
0.44
0.22
0.41 10.00
0.16
N/A
0.89
200
N/A
0.30
0.43
0.47 20w
0.25
0.40
0. 0.12
N/A
0.91
collins
100
N/A
0.72
0.84
0,90
0.44
0.91 10.00
0.28 0.28
NIA
0.94
0.94_003
200
mm94
0.64guus
0.87
0.92
0.44
0.93
0.23
N/A
0.96 0.96_0000
50
2.89
0.74gu04
0.71
0.88
0.10
0.88_
0.45
N/A
0.93
100
0.96
0.67
0.81
0,91
0.11 2000
0.92::002
0,22
N/A
0.97
0.97=001
texture
200
0.96
0.562004
0.80
0.93
0.12+001
0.95-20.01
0.08
N/A
0.98
500
0.97
0.63
0.84
g,93
0.1 0.14
0.96
0.1 0,000
N/A
0.98_oon1
Average rank
3.24
6. 6.76
5.91
4.12
8.42
3.97
8.2 4
3.30
1.04
35

---

Table 17: KS test between real train data and synthetic data eight real-world tabular datasets with varied real data availability. We report the mcan + std result and average rank across datasets. A higher rank implies higher fidelity. Note that "N/A" denotes that specific generator applicable, and the rank is computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. TabEBM achieves the best overall performance
not
against benchmark generators.
Datasets
Naa
SMOTE
TVAE
CTGAN
NELOW
TabDDPM
ARF
GOGGLE
TabPFGeen
TabEBM
N/A
0.72gmm
0.75
g.8l
0.63
0.80
0.44
0.84
0.87
50
0.90
0.872000
0.87
0.89:a0l
0.62+0.01
0.89-2000
0.73
0.91 10.00
0.93-000
protein
100
0.922mm
0.88
0.91
2.90
0.60
0.91 10000
0,60
0.94 2000
0.94 0,94_000
0.94
0.87
0.92:2000
0.93
0.59 2001
0.93
0.58
=.95
0.95-000
500
0.95
0.83gum:
0.92gnme
g,93
0.59
0.94 2,94
0.63
0.95
0.96
20
N/A
0.71
0.73
0. 0.79
0.85
0.85
0.85
0.94
0.90
50
0.92=n00
0.87
0.88
0,91
0.64
0.90
g.73
0.93=0000
0.94-000
fourier
100
0.94
0.87200:
0.92+a.0
0.93
0.63
0.93
0.62
0.95
0.95
Armost 10 classess
200
0.95
0.83gum
0,92
0,94
0.62
0.94 2000
0.61
0.97
20000
0.96-_0o
500
0.96
0.81ga00
0.94
0,95g000
0.62
0.95=2000
g,63
0.97 =2000
0.9 0.97_000
20
0.63
0.62
0.64
0.64
0.56
0.63
0,65
0.59:2o.2
0.70
50
0.57=000
0.57
0.59
0.60
2.48
0.59
0.63
0.61
0.73-000
biodeg
100
0.56gm0s
0.55
0.57
0.59 2000
0.46
0.58
2..8
0.59 0.59
0.59 2000
0.73 0.73_0m
200
0.53
0.52gam:
0.53
0.56ga00
0.43
0.55
0.55
0.58
0.72
500
0,53
0.50gam
0.52
0.55
0.43
0,56
0,56 0,56
0.57
0.72
20
0.67=
0.63
0.64
0.66
0.54
0.65
0.57
0.67 20,0
0.76
0.69
0.64gam
0.65
0.67 2000
0.51 2o0e
2.67
0.56
0.72
0.79 -0m1
steel
100
0.692a02
0.63
0.65
0.67
2001
0,50
0.65
0.55
0.71
0.79
200
0m70
0.61
0.66
0.69
2mm
0.50
0.65 2.68
0.55 goor
0.71 1000
0.79 000
500
0.70
0.62+am2
0.66
0.68
0.49
0.65 10.5
0.58
0.7 0.74
0.80 0.00
20
0.86
0.82gmm
0.82
0.86
0.74
0.86
0,63
0.89 10:001
0.91
50
0.92-am
0.86200:
0.88
0,90
2.84
0.91 -0.01
0.68
0.93
0.94
0.94_000
stock
100
0m94
0.86gam
0.90
0.92
0.88 1o0e
2.93
g,63
2.95
0.95
200
n.
0.86:a0:
0.90
0,93
0.92
0.94=0000
0,63
0,96
0.95
More than 10 classes
50
N/A
0.70
0.69
0.73
1.65
0.72
0.63
N/A
0.78 0.78
energy
0.74
0.74
4.60
0.74_.001
0.63
200
N/A
0.71
0.74gam
0.75
0.67 p.67
0.75
0,63
N/A
0.83
100
N/A
0.85
2.89
0.90
0.90 0.82
0.65
N/A
0.93-0000
collins
200
0.93
0.83gumt
0.91
0.92
4.80
0.92
0.63 goos
N/A
0.94 0000
50
0.92
0.86gam
gn88
0.90
0.57 00.0
0.90
Lgoo
N/A
0.93
100
0.94
0.86:00:
0.91
0.92
0.61
2002
0.92=2o01
0,63
N/A
0.95-o00
texture
200
0.96
0.83200:
0.91
0,93
0.62
0.94
0.60
N/A
0.96
500
2.97
g085
0.91
0.93
0.61 100r
0.95_000
0.64
N/A
0.97 2000
Average rank
1.91
6.97
1.76
3.97
8.33
4.15
7.55
3.21 22.16
1.15_0036
36

---

Table 18: x² test between real train data and synthetic data eight real-world tabular datasets with varied real data availability. We report the mean + std result and average rank across datasets. A higher rank implies higher fidelity. Note that "N/A" denotes that specific generator applicable, and the rank is computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. TabEBM achieves the best overall performance
not
against benchmark generators.
Datasets
Niai
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF GOGGLE
TabPFGen
TabEBM
20
N/A
0.02zuu:
g.08
0.19
0.02
0.05
0.02
2.33
0.92-007
50
2.95
0,84g00s
0.50
0,92
0.01 1000
0.98_.o0 2000
0.53
2.63
0.96_nox
protein
100
0.86
0.621amn
0,53
0.83
0.01 2000
0.89
0.89200s
0.27 0.27
0.70
0.91 0.91_0m
200
0.80
0.46gam
0.46gam
0.77
0,01
0.76
g.02
0.66
0.81
500
0.62
0.25
0.36
0.61 #004
0.01 10.00
0.57-2005
0.01 0,01
0.65
0.70
20
N/A
0.02:aoz
0.05
0. 15
0.37 20.04
0.35
0,36
1.00
1.00__0.00
50
2.99
0.87
0.52
0,97
0.01 10000
0.99 :0001
0.49 0.49 2010
0.74
0.99 0.99_0m
fourier
100
0.962am
0.75
0.69
0,95
10:00
0.98
:0.00
0.16
0.82
0.97
Af most 10 classes
200
0.92
0.41
0.59
0,92
0.01
0.95
20.02
0.02
0.85 0..5
0.95
500
0.80
0.14ga04
0.59
0.76
0,01
0.84
g,01
0.81 =0.04
0.84 onn
20
g.23
0.21
0.16gn04
g.28
0.08
0.28 20,07
0.12
0.29 20.00
0.71 ...
50
0.39
0.33
0.28
0.41
0.05
0.45-1005
0.15
0.44_2000
0.75
biodeg
100
0.35
0.26gum
0.30
0.38
0.04
0.42:20ms
0.08 0.08 2000
0.37 20.33
0.67 0014
200
0.25
0.192nns
0,24gnas
0.30
0.03
0.31 20.06
0,02
0.37-20.6
0.59 -0.8
500
0.22:20.5
0.10
0. 0.17
0.25
0.02:10.00
0.23
0,02+0000
0.26
0.44_o.00
0.44
20
0.37
0.32gaa5
0.32
0.40
0.04
0.40
0.23
0.34 _o.13
0.81
0.68
0.50gums
0.51
2.64
0.03
2.67
0.10
2.49
0.85 0m06
steel
100
0.61
0.37
0.47
g.61
0.03
0.61
0,06
0.51 =0007
0.81
200
0
0.60=a04
0.23
0.42+006
0.60=aa5
0.03
0.53
0.02
0.52-2007
0.77 0006
500
0.46
0.172005
0.35
g505
0.03
0.42::0.04
0.02
0.48
0.69 0.00
20
0.56
0.50
0.40
0.63
goow
0.1 1o.rs
0.55 2.55
g.43
1.56
1.00
stock
50
0.85 0.9
0,88
0.99
2a09
0.12 10/0
1.00:0000
g:
0.87
0.99-0003
a.00=
0.64
0.89
:0.00
0.13
0.91 10.10
0.99 0.99
200
n.
0.58
0.76
0.98
0.7 10:22
1.00
0.10
0.99
.0.9
0.99 0.99__o.0
More than 10 classes
50
N/A
0. 0.14gu
0,26
0.35
0.17 1000
0.41 22.14
0.19 0.19
NIA
0.80 2..0
energy
100
N/A
0.32+a12
g.35
0.13
0.30=00.0
0.06
N/A
0.92-o01
200
N/A
0.15
0.30
0.39
0.1 25007
0.28
0.03
N/A
0.96
100
N/A
0.61aams
0.73
0.87
0.10
0,90
0.20
NIA
0.89-0004
collins
200
0.75
0.35
0.62
0.76ga00
0.07 100m
0.78
0.05 10o4
N/A
0.80
0.10
0.79
0.63
2.94
0.02
0.99 20.02
0.47
0.93
100
0.97
0.51
0.67
0.92
0.02
0.94
0.94_100
0.17
N/A
0.97
texture
200
0.86
0.28
0.55
0.89
0.02
0.93-.007
0.93
0.00
N/A
0.91
500
0.74
0.2
0.51
0.73
0.02
0.73
0.00
N/A
0.82
Average rank
1.5
6. 88
6.03
3.55
8.30
2.82
8. 1818
4.27
1.45
37

---

D.6.2 Similarity between Real Test Data and Synthetic Data
Table 19: Inverse KL between real test data and synthetic data on eight real-world tabular datasets with varied real data availability. We report the mean + std result and average rank across datasets. A higher rank implies higher fidelity. Note that "N/A" denotes that a specific generator was not applicable, and the rank is computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. TabEBM achieves the best overall performance
against benchmark generators.
Datasets
Naa
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabEBM
20
N/A
0.26
0.26gam
0.32
0.09
0.34_2o0x
g,08
2.35
0.52_.os
50
0.78=002
0.82:002
0.63
0.71 2004
0.08
0.80=005
0.52+000
0.02-2004
0.75
protein
100
0.88
0m
0.76gn04
0.83
0.08 g000
=.87
g,33
0.78
0.85
0.85-om
200
=.92
0.75
0.81
0.91 =000
0.00
0.91 =0,01
0.12+aol
0.89=0.02
0.92-000
500
0094
0.68
0.86
0,93
2.08
0.94
0.13 0.13
0.94
0.95
20
N/A
0.14
0.18
0,20
0.21 #0.02
0.21 :0001
0.22
0.24
0.48
50
0.84
0.78
0.62gnos
0.77
10:00
0.85
0,48
0.66
0.79..om
fourier
100
=.91
0.72+005
0.76
0.88
0.08
0.90=.001
0,20
0.81 =0.02
0.88 0.88
most 10 elasses
200
0.94
0.58
0.79
0,93
0.09
2009
0.93
0.08
0.90
0.93_00
500
0,96
0.50ga02
0.88
0.93
0.10
0.95.20.1
0.09
0.95
0.96
20
0.43
0.44
0.41gam
0.41
g.33
0.44_20xx
0,36
0.45
0.57
50
0.60
0.60=-00
0.59
0.53
0,55
0.31 4000
0.57
#:000
0.60
0.71 0..4
hiodeg
100
0.65
0.65
0.62
2.63
2000
2.64
2000
2.65
0.77 0000
200
0.71 =002
0.66:002
0.66
0.65
0.31
0.68
0.33
0.73
0.83 _.03
500
0.77
0.64guuz
0.69
0.72
2.25
0.69 2003
0.35
0.76
0.88 0.08
20
0.47
0.45
0,42+am
0,44
0.23
0.46
#0.4
0.42-20.04
0.70
50
0.65
0.59
0.58
0.60
0.21 10:0
0.63
0.30
0.02
0.83
steel
100
0.70
0.59
0.62
0.66
0.21 +0.01
0.66
0.29 #000
0.72-20.44
0.89
0000
200
0.73
0.55
0.66
0.69 2000
0.22
0.68 20.0
2005
0.75
0.91
500
0.74
0.55
0.66
0.69.am
0.22
0,70..o01
0,27
0.78.2005
0.93 ..mt
20
0.50=:09
0.50gam
0.41
0.47
0.25 40.04
0.54
0. 0.40
0.35 2005
0.65
0.65-0000
0.80
0.68
0.68
0.76
0.34
0.86
0.33
0.69 =0.00
0.85
stock
100
0,86
0.61
0.73
0.85
0.44
0,90
0.18
0.84
0.91
200
0.59
0.75
0.90
0.67 10.00
0.94 2000
0. g,15
0.94
2003
0.96
More thon 10 elasses
50
N/A
0.26gu0
0.33
0.36
2005
0.46
0.22
N/A
0.77 0003
energy
100
N/A
0.27
0.40
0.43
0.22
0.39-
0.16
N/A
0.87-000
200
N/A
0.30
0.41
0.46ggo
0.24
0.39
0. 0.12
N/A
0.89
collins
100
N/A
0.68
0.75
0. 0,79
0.43
0.81 10.00
0 0.28
NIA
0.78
200
g.87
0.62gam
0.81
g.88
0.44
0.88 20.00
0.22
N/A
0.87_00m
50
0.82
0.80
0.70
g.80
0.1 0.11 jooo
0.92.1001
0.48
N/A
0.87
100
0.89
0.69
0.79
0.89 2.89
0,13
0.93
0,23
N/A
0.92
texture
200
0.93=
0.58
0.79
0.92=a01
0.14
0.95
0.10
N/A
0.95-0001
500
0.96
0.64
0.85
0.93
0.15
0.96
0.12
N/A
0.97
Average rank
2.94
6.03
5.82
4.39
8.48
3.00
8,24
4.45
1.64_103
38

---

Table 20: KS test between real test data and synthetic data eight real-world tabular datasets with varied real data availability. We report the mean + std result and average rank across datasets. A higher rank implies higher fidelity. Note that "N/A" denotes that specific generator applicable, and the rank is computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. TabEBM achieves the best overall performance
not
against benchmark generators.
Datasets
Naa
SMOTE
TVAE
CTGAN
NELOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabEBM
N/A
g.69
0.72
0.75gam
0.61
0.74
g.41
0.77
0.81=oo:
50
0.882am
0.87200:
0.87
0.88
0.61 10001
0.89
0.73
0.86
0.88-001
protein
100
0.90
0.87
0.89
0,90
0.60
0.91 1001
0,65
0.89 0.09
0.91 0.91_0m
0.92.am
0.86200:
0.90
=00l
0.59 20.1
0.92=0001
0.58
0.91 10.01
0.92-000
500
0.922mm
0.82gum:
0.90game
0.91
0.58
0.92
0.63
0.92.000
0.93
20
N/A
0.67
0.69
0.73
0.75
0.75
0.75
0.76.00.1
0.81
50
0.89
0.86:a0:
0.88
0.64
0,91 =0:00
g.73
0.87
0.89
fourier
100
0,92-am00
0.85
0.90
0.91
#0,0
0.62.40.0
0.92.10.0
0.61 +:002
2.90
0.91 -0,00
AI most 10 classess
200
0.93
0.82
0.91
0,93
0.62
1.93
0.60
0.93
0.93_000
500
0.94gn00
0.80
0.92
0,93
0.62
0.94 0.9400000
g,63
0.94
0.94 0.00
20
0.61
0.61aa0
g.63
0.63
0.55 20.0
0.62
0,64
0.56
0.67
50
0.56
0.57
0.58
0.59
2.48
0.58
0.63
0.59 20.04
0.71 0.71_0001
biodeg
100
0.55
0.55
0.57
0.58
0.46
2..8
0.59 0.59 aooe
0.58 2o.8
0.71 _00
200
0.53gam
0.51
0.53
0.55
g.43
0.55 2..0.
0.55
0.57
0.72
500
0,53
0.49
0.51 g.51
g.54
0.43
0.55
0,56
0.57
0.72
20
0.65
0.622am2
0.63
2.65
0.54
0.64
0.56
0.64
0.73 0.73-000
0.68
0.64gam
0.65
0.67
20or
2.68
0.56
0.70
0.77 0001
steel
100
0.68
0.63
0.65
0.66
0,50
2.66
0.55
0.70
0.78 0.78_o.0
200
0.69
0.61
0.66
0.68
0,50
0.65 2.68
0.54 goor
0.71 1000
0.78 000
500
0.69
0.62+am2
0.66
g.68
0.50
0.6 0.64:20.01
0.58
0.73
0.79 _.00
20
0.83
0,81
0.84 0.82
0.74
0.84
0,64
0.83
0.86
stock
50
0.892002
0.84gau2
0.87
0.88
0.83 200e
0.89 20,2
0.67
2007
0.88 =088
0.89
0.00
100
0.91
0.84gum
0.88
0.90
0.87 1000
2,90
0.62
0.91 20.0
0.91
200
n.
0.82
0,90
0.90
0.91 =000
0,63
0.92
0.92..om
More than 10 classes
50
N/A
0.69
0.70
0.
g.72
0.64
0.72
0.62
N/A
0.76
energy
amm
0.74
0.75
4.60
0.75
0.64
0.81 0001
200
N/A
0.71
0.74
g.75
0.67 20/e
0.76
0,63
N/A
0.83
100
N/A
0.83200:
0.88
0.90
0.81 2004
0.90
0.65
N/A
0.90
collins
200
0m91
0.82gamt
0.90
0.91 go0
4.80
0.91 1001
0.63
N/A
0.93
50
0.90
0.87
gn88
0.9
0.55
0.92
0.73
N/A
0.92
100
0.92=nni
0.86:00:
0.91
0.92
0.60
0.93
0,64
N/A
0.94_oo0
texture
200
0.94_am
0.82200:
0.90
0,93
0.62
0.94
0.60
N/A
0.94
00.0
500
0.95
0. 0.84gam
0.91
0.93
0.61 1000
0.95 0.95_
0.64
N/A
0.95 00.0
Average rank
3.97
2.09
5.52
3.76
8.27 +1.21
3.27
7.45
4.39
1.27
39

---

Table 21: x2 test between real test data and synthetic data eight real-world tabular datasets with varied real data availability. We report the mean + std result and average rank across datasets. A higher rank implies higher fidelity. Note that "N/A" denotes that specific generator applicable, and the rank is computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. TabEBM achieves the best overall performance
not
against benchmark generators.
Datasets
Niai
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabEBM
20
N/A
0.01
2.01
2.00
0.01 2000
0.01 20:00
0.01
0.02-2011
0.06-003
50
0.26gans
0.32
g.09
0.17
0.01 1000
0.25
0.22
0.05_0.x
2.15
protein
100
0.39
0.33
0. 1818
0.01 1000
0.34 0.34_
0.13
0.12
0.26
200
0.48
0m30
0,28
0,48
0,01
0.44
g,02
0.34
0.43-o06
500
0.54
0.24g007
0.33
0.60
0.01 #0.00
0.55
0.01 0.01
0.53
0.58-000
20
N/A
0.00
0.01
0.01 20:00
0.01 10:00
0.01
0.01 0.01
0.01
0.10-0044
50
0.42
g.45
0.15
0.31
0.01 1000
0.39 2000%
0.29 0.29 2:000
2.10
_.33_00m
fourier
100
0,58
0.44gam
0.32
0.52
0.:00
0,48
0,08
0.26
0.49_000
At most 10 classes
200
0.67
0,28
0.38
0.68
2088
0.01
0.60
0.02
0.46
0.6 0.60--oa
500
0.76
0.15
0.55
0.72ga00
0.01
0.71 20.05
0,01
0.69 20.04
0.74_om
20
2.05
0.05
0.04
2.04
0.03
0.05 2.05
0.03
0.10
0.13__00
50
0.13
0.12
0.07
0,08
1004
0.02
0.08-200x
0.06
0.08-20.4
0.14 0.14_005
biodeg
100
0.15gmms
0.14gums
0.10
12
0.02
2.12
0.04
0.07 2000
0.18 0004
200
0.18
0.15
0.14gam
1.19
0.03
0.18
0,02
0.14
0.28
500
0.25
0.13
0.21
0,28
0.03
2.28
0,02+0000
0.23
0.38
20
0.13
0. 0.16g004
g.09
0. 1000as
0.03
0. 1o.o
0. 0.12
0.07 2oot
0.29
0.26gau7
0.24gumn
0.17
0.21 2006
0.03
20.04
g.05
0.17
_.43_o0m
steel
100
0.32
0.23
0.24
0.3 ga00
0.03
2.33
0,04
0.29 0.29.000
0.49_o.07
200
0.36
0. 0.17
0.29
0.34
0.03
0.36
0.02
0.35
0.53
500
0.37
0.15
0.28
0.36
0.03
0.36
0.02
0.38
0.57 00.06
20
0.3
0.38
0.22
0.25 goos
0.10
0.33
0.42
0.11 2o0m
0.41 10.19
50
0.60
0.56ga
0.44
0.54
0.10 4.1000.0
0.73
0.3 1:014
0.41 20.15
0.76 0.76-0.10
stock
=.71
0.40
0.53
0.68
0. 12:0006
0.85 =0,05
0.13
0.65=0.12
0.87
200
0.86
0.45
0.60
0.9 gan
0.35
0.97
0. 0.10
0.92=0008
0.97
More than 10 classes
50
N/A
0.15
0.28 0,25
0.17 10:0
0.40
0. 0.15
NIA
0.78 0.78_
energy
100
N/A
0.10
0,3
0.34
0.14
0.30=
0.06
N/A
0.92.omm
200
N/A
0.16
0.30
0.38
0.1 2
0.28
0.03
N/A
0.96
100
N/A
0.23
0.21
0.25
0.05
0.24
0.07
N/A
0.18
collins
200
0.32
0. 0.16guus
0,24
0.38
g008
0.06
0.33
0.02
N/A
0.31 2000
0.33
0.44
0,21
0.29
0.02.2000
0.55
0.27
0.41=004
100
0.44
0,27
0.27
0.48
0.02
0.54_100
0.07
N/A
0.49
texture
200
0.51
0.19ga10
0.34
0.58 0.58
0.02
0.64-000
0.00
N/A
0.59-000
500
0.63
0.21
0.49
0.67 2008
0.02
0.64
0.00
0.66
Average rank
3.06
5.45
6. 6.
3.64
8.36
3.18
7.76
3.33
2.06
40

---

D.7 Results on Privacy Preservation
D.7.1 Downstream Accuracy in Data Sharing
Table 22: Classification accuracy (%) aggregated over six downstream predictors, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean I std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of specific generator. Different from Table 1, "-" denotes a generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. The results of these inapplicable or failed generators are computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes. TVAE learns the joint distribution p(x, y) and fails to maintain the original training label distribution. TabEBM achieves the best overall performance against Baseline and
benchmark generators.
Datasets
Naat
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
GOGGLE
TabPFGen
TabEBM
20
N/A 16.38_1344
13.064359
12.99.416
12.64-206
19.42.23
12.88
33.11
33.97:34
50
27.29_144
14m
13.20
14.04_1a
29.34.44
13:05
54.82 1m0
55.83 1:35
protein
100
12.46
40.04.4.:
26.65
12.80
17.65-325
35,90 35.90a539
13.55230
71.63-295
22.99
45.33 1m
pm
32.5
14.07 LTW
20.79
L431
11.68170
w 91.19
84.29 1200
500
55.24_5.00
44.35
12.762278
21.63_4.00
54.26.33.7
11.09
48
21
20
N/A
13.30
10.72
10.03
17.14:415
10.29
33.87
37.06
50
+3.56
N/A
0.884251
11,96
28 23.3
11.52
$6.88,2210
fourier
100
64.06 1:34
34,80
23.35
10.85 Li1
17.68 -3442
32,59 14:00
9,82
64.42
64.93 1:00
200
70.78
40.49...41
32.98,530
10.28.2374
28.63_.4m
39.
9. 9.55
71.37
22.01
500
1448
46.83_
1631
11.13 1247
27.25 6.01
47.19 12:0
10.3
75,86 (1.1
76.58 11:54
most 10
20
68. 64
64.07-139
53.60
54.58
48.39-2.73
58. 58.69
48.652930
69. 14.184
69.66..5.5
22.08
67.11
62.21
55.12
4..86_1154
70. 14
42.14
73.53
23.96,2313
biodeg
100
75.6 =244
20.901405
70.334531
58.08
48.78-102
70: 10:792218
49. 15:231
76.65
76. 76.56-229
200
78.97
71.54:2444
714424430
55.78
47.63
72.74.54
50.75
79.66
79,80
500
4442
74.57
76.32+299
52.78.417
47.31
75. 25.67
48.05
81.36
10
20
57.55 pm
54.39
52.13
51,28
52.03
49 49.25
63.27
63.30,
50
39.06
56.70+496
53.24
49.18-467
57. 16:44433
49 19.90+3.0
78.55-5.17
29.99
steel
100
72. g1
11
39.37.350
52.79
45.01_5.
57.26
49.66.156
90.12_170
92. 92.33, s7
200
77. 23,5
65.45-407
63.314463
51.022224
43.71-1.51
61.4 61.41
50.20:33.
94.61
95.54.144
g4.21
40.26
70.62,55.0
49.97
46.98_4.30
66.33
51.60
g6.31
97.04:1.1
20
81.
24x2
51.71 51.71 69.35
67 67.05
75.94
16:915
48 28.55
82.55
83.60
50
87.
77 17447
76.07
69.12
70.61
85,99
78.38 1856
49.74147
88.09_137
88.49
100
89
2::30
31.18.434
18:44
72.05 13
88,27 2.54
84.02:210
a1.07
90.13.1.57
90.58
2000
91.11
84.05
82.12
15.44_141
89.92_1.5
85.66_336
49.74
91.09
91.07
.0
1.17
g.20
4.21 1m
1.
1.52
NIA
23.80,2200
More than 10 classes
energy
100
N/A
7.66
5.522114
4.08-140
9,87
2.01
NIA
30.15
2010
N/A
7.57420:
6.9221
3.42
11.85
4.18
NIA
35.74:359
N/A
5.51
4.58
11.74
5.34
3:77
N/A
23.12
collins
200
17.60
1135
4,70
13.64_
5.46
3.92
N/A
16.80
50
75. 15
23.86-805
12.00a419
12,162320
17.18-534
16.8224.16
9.634275
NIA
78.844335
100
83.77
26187-419
14.05
13.95
20.08 20.08_1.1 1.5
23.82.596
10.21
NIA
85.88
Texture
200
87.96 87.96.1.00
21.59
15. 15.36444
12.17-457
20.59-506
42.28 42.28a551
9.524291
N/A
88.844165
91.65 11:14
24.48.
26.45
12.37
20.07
57.94.4m
10.22
NIA
91.361111
Average rank
2,76
4,32
6.18
7.48
7.03
4.91
8.52
2.36
1.24
41

---

Table 23: Classification accuracy (%) of LR, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of specific generator. Different from Table I, "-" denotes generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. failed generators
computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes. TVAE learns the joint distribution p(x, y) and fails to maintain the original training label distribution. TabEBM achieves the best overall performance against Baseline and benchmark generators.
The results of these inapplicable
Datasets
Nwn
SMOTE
TYAE
CTGAN
NELOW
TabDDPM
ARF
GOGGLE
TabPPGen
20
NIA
14,51 1355
13.00
12.08
13:83
22.46
12.52,22e
38.00
38.04,234
50
61.15g4m
24.43_131
16.81
12.55
14.74.4.
33.77
12.26.444
63.01
62.94 10
pretein
100
78.16
40.22 Lm3
27.14
12.40.sm
19.34
40.99 1534
12.33
80.54 1::2
80.18 12
200
13.
45.70
45.70_129
34.17a6m
13.87
22.01
44.76:445
12.78
90.59
90.09
500
94.29_117
60. 60.39_231
47.8749.9
12.582306
24.6945.9
58 58.91
9:794545
95.86_1.9
95. 18
20
N/A
11.64
10.16
8.48
18.75
g1
42.98 1:144
43,04.5
50
58.24-205
N/A
9.82=445
13.48
33.97-371
12.00+292
60.30_1.51
60. 60.28
fourier
65.
28. -.
21.26
11.24
19.72
37.64
11:34
67.36
67.38
At most 10 classes
200
70.74 70.74-213
31. 31.50-411
28.8644422
10. 10.452
33.582355
42.7542257
7.524205
72.20=302
72. 12.18 18
500
46.8 46.84-2.9
41,18
10.60.xm
31,88
48 48.67
10.56
75.58
76.00:220
69.93_5m
66.922716
102
15
11.15
12
70.78
50
74.71
70.19
62.90 1674
56.85
42.74
73.38
$1.52
75.67 13:31
76.47
biodeg
100
77. 21.48_188
71.77
71.424327
59.17 59.17
24.24
74.482244
48.03212.5
77.
78.34_221
200
1.77
75. 15.37
72.61 4599
56.71=121
164471
75.09
12.94-11.50
81 11:21=200
81.50..1.4
500
82.68
77.92
77.55
$4.90
46.53
77.87
46.40_1255
82.38
82, 14
56.80=546
14.06=11.24
$4.41
51.402633
54.38:454
48. 48.324469
66. 66.75
50
66.80 1m:
11.11
58.25 2667
52.95 22.95
47.07
61.31
47.8
93.51 11:1
92. 13
steel
100
79.38
64 64.64_1.99
60.57
54.40 54.40=567
42.51
58 58.8643356
50.95
99.21
99. 10.117.2 1748
82.66-351
71.78_304
65.44.55a
$1.72.441
38.19
63.31a5a
$3.46.22
99.45.uar
99.51 99.51.00
500
90.21
76.49_.00
75.41
48.71
46.00
72.11
$2.55
99.70 99.70gm07
99.72,00
20
80.31
71.68 .r.rs
54,58 15.01
70.64
71.05
68.03
49.84_197
79.58 11
80.33
$1.28_2277
75.75_1384
69.67 67 4314
26.99.639
77.72.449
24.44
29.01
$2.37 +5.
22.006622555
stock
100
83.90=1.8
78. 78.79933.5
77.3 77.37
75 23.64
80.43.530
78 22:22444
49
60
83.65
83, 13.56
200
83.61
79.31__2
80.20
16.37..193
79.32
12.89
48. 18.18,,.
83.69 1141
83.82
More than 20 elasses
energy
100
50
N/A
N/A
7,51_114
5.79 12:0
7.16
6. 6,15
5.89 1.9
3.42
4.88
10.67
8.72
4.52
4.03g133
NIA
NIA
21.56 11:00
27.59
7.82+219
6.63-2.1
3.4821.4
12,964212
4.34+144
N/A
33.01=224
100
N/A
5.33
5.49
12. 12.30
5.98
3.61
NIA
14.02:244
collins
200
18.
2.36
5,13
14,70
6.04.uus
3.28
N/A
19.11
86.20
2672
25.72
13.32.446
13.86
23.90
18.17
10.1
NIA
28.46
100
93.17 17=2m
26 26.04-2224
12.344547
12.44=557
27 27.672630
22.55
22.554555
12.004529
NIA
94.23
texture
200
95.70_124
16.65
17.15
13.14..40
29.67
43.54
43.54
11.12
N/A
95.99.111
500
97.17 2033
19.00=1043
27.24
11.68
27.75
60. 15
10.95
NAA
96.53
Average runk
2.82
4.70_aoa
6.39
2.48_00s
6.79
4.64
8.52
2.24
1.42.0s
42

---

Table 24: Classification accuracy (%) of KNN, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of a specific generator. Different from Table "_" denotes a generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. The results of these inapplicable or failed generators are computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes. TVAE learns the joint distribution px,,)) y) and fails maintain the original training label distribution. TabEBM achieves the best overall performance against Baseline and benchmark generators.
Datasets
Nea
SMOTE
TVAE
CTGAN
NFLOW
T5NDDPM
ARF
GOGGLE
TapPTGen
TabEBM
20
N/A
16.84_
12.84-1.
11.26
11.63
16.53
11.76
34475
35,76
27.34_am
1m
13.25
12.03gm
24.09
12
5344
protein
100
69.
29.44225
39.23-136
22.23-130
12.64
16.71
30.642430
13.66=12
67.23-245
67. 67.35-220
200
27.12
41.50:414
27.68-137
14.16:410
20.29
36.01:174
11.91
75.56
16.17
500
50.56-532
34.07
13,44
19.904306
46.40g3.8
11.99
83.63
20
N/A
19.60 4.25
11.06
9.16
15.58
9.78
12,66
42.78
50
60.16.1:8
NIA
9.74
11.666239
24.32:4499
12.86
58.5221.1
58, 58.56
fourier
100
66.542215
18:5.0
19.86
10.68:2444
18,4242340
27.60 27.64:426
9.48
64-4222
64. 64.98
At most 10 clavres
200
71.08 j2:0
42.72 2m
31.68 .0:
9,70
26.90 26.96
34,32 34.32
9.76
70.00 70.00
70.50
500
21.0
47.58_33
42. 12
10.00 in
26.18
41 41.87
10.88
73.46 80
g1
11 11.1
24.27
52.02
47.8 87187
2004
=7.41=12m8
67. 67.89..4s
69. 69.62254.2
50
72. 84 12
66.
61.89 1307
$2.26
50.78 1831
67.72
53.48
72.01 1431
73:77
biodeg
100
75.82-22.0
86-136
70.02-415
48.67 +436
69.39.225
19.25
74.77=209
75.
200
79.67:3015
70.25
=1.89=121
53.54
51.402222
70.21 =3.57
49, 49.42
77.78=242
78. 78.23--206
500
82.51
12.72
$2.922557
46 16.1444419
73.57
20.03
80.55
81.15
15
56.75 mM22
84
19.9
42729
52.67.1550
49.23
10.71
69.36 L41
69.72 49
60.43_si1
57.6 16
$4.41
48.61
57.24 47.24
49.66
82.03
80.57
steel
100
76.33 19
63. 34_222
60 89 8983
$2.24_116
42. 42.38-663
58.01
$1.17=1m
87.79
87. 87.76
200
11.7
68.00.2245
66.3 24277
50.19.41c
43.8227744
63.29..404
$0.99
90.90
91.09 $1.75
500
85,06
73.24_
72.49 1a
49.19
45.77
68.81
52.45
92.81 92.81.11
92.83
20
84. 25
66 66.05
52, 15.0
58
28.69
77 77.28
28.03
45. 13-152
84.45.242
84.69
stock
100
91 93
1235
80.87
75.40_xxm7
67.6 jamr
78.37
67.33
91 11.03
88.94115
77.67 14.M
84.53
48.55
53. 33.19-11
11:s
91.98 20
11
92.35 1:
89, 390,00.1
200
93.46.00.9
84.65=151
81.6 81.6422m
40.56:241
91,81
85 85.584224
49.98=11.9
92.53
92.9 92.941.0.00
6,75
1.88
4.71
6.06
2.63
25.36_2219
More than 10 ciosses
energy
100
N/A
7.53
5.33
3.68
9.05
4,37 4,37
N/A
29 039633.22
200
N/A
7.22
6.01
3.30
10.56
N/A
33,85
100
5.61 =008
4.32
13.46
4.71
3.802mm
N/A
15:20
collins
200
19.94
5.24
4,49
15.29
4.58
3,89
N/A
17.66
50
78.67
12.36
11.19
15.85
13.67
9.05
NIA
75.57
100
85.31:24
25.800-3:
13.82-118
11.67
19.32
25.54 25.54
9.09=2.0
NIA
84.69
texture
200
88. 88.17
18.33_141
13.85
10.55
23.17
42.92.667
9.07
NEA
89.16 1175
500
90.78
29.29-1.0
24.91
10.23
23.85
47.58
10.12.255
91.23
Average rank
2.03gn59
4.39_n44
6.03_1m0
7.70
6.97
5. 5.30
g.33
2:73
1.52.051
43

---

Table 25: Classification accuracy (%) of MLP, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of a specific generator. Different from Table "_" denotes a generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. The results of these inapplicable or failed generators are computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes. TVAE learns the joint distribution (x, y) and fails maintain the original training label distribution. TabEBM achieves the best overall performance against Baseline and benchmark generators.
Datasets
Nea
SMOTE
TVAE
CTGAN
NFLOW
T5NDDPM
ARF
GOGGLE
TapPTGen
TabEBM
20
N/A
15.81
12.08.4.
13.06:112
12:93
20.17:444
12.98
26.01
36.23
56.85
26
14
13.68 s
14.92
31.36
1
58.69
28
protein
100
75.
86430
41.60-44
25.
25.78-4m
11,34
20.82+455
40,31
14,54
77-47=339
77,56-318
200
87
27.85
50.87-6as
32.49-1.6
12.90-17
23.85
45.40:aa1
10.24
:0.01
89 89.48-2210
500
62.81
47.222244
12.00
60.31
10.41
96.26
96.03
20
N/A
12.16
10.56
10.38
19.66
11.04
34.40
35,04 1100
50
52.722a.
NIA
9.42
13.78
33.94
10.88
55.122151
25,30
fourier
100
87-5255
16-301
21 21.44-115
10.884111
21 21.964224
29.68
8.12
63.54
64.08
At most 10 clarres
200
68. 12
42.118
30.56
10.94
33.80
43.9 43.92.1217
8:46
71.76
71.36
500
11
50.48_403
45.94_1.5
13.10
35.181584
51.10
2.66
76
27
6435
62.24-xa5
53,56
25
45287
27.764442
45 45,98.1122
72.04
72.10 :2.10.440
50
73.48
65.96 6.31
62.15 1111
55.84
45.55 185t
12.40
49.95 19-95
77.20
77.24
biodeg
100
77
70.20-5557
27,99
49,10
71.42:2.99
45.5225al
18.58
78,
200
8 31.30
72. 72.26-:536
24559
45.75
44.37=2227
73.8 73.82:433
48.45
82.06=157
82.25 =1.0
500
83. g3.5
74.3624322
77. 27.55
53.37
43.97
76.51
47.04
83.6321.
83.33
15.00
11.47
12.0
$2.76
51.25 51.25 14.t
47.90 L1
64.34.A21
64.33
66.
62.02 5.08
57.41 11
14.51
50.58
59, 85 15
50.78
83,06 14:0
82. 82.38
steel
100
76. 17
63 63.05-4.11
60 6076222711
54.81
44 44.6442229
59 64
48. 48.93_1.
95. 36236333
95.455
200
2217
(8.45
64.73
50.83
39.73
62.36 62.36.250
47.89_171
98.3 98.34
98, :0at
500
73.89
71.48
49.32
43.65
68. 18.12
53.56_420
99.56 99356.031
99.45 1.
20
82: 24:6
71.78-1.33
11.09-
68 68.462157
76.71
62. 13:133
12.68-11.
83. 23.8
83.91
stock
100
90 85 72
12
81.612337
237
79. 19.76
4mm
13.18
71.03
90.172116
87.47
85.8 25.83
50.41=147
50.41
48.79 1m17
91 60.001
11 sn
91.72
961 12:0
200
+0.9
84.67=245
82.92=2m
74.97
91.21=1100
87.06x218
14.90=11.8
92.24=055
92.00
More than 10 ciosses
energy
100
N/A
1.77
7.44-338
5.64
5.75
5.34
3.68
4.30g200
10.38:157
1.28
4,29 4.29
4.46
N/A
23.91 :1
29. 29.24...4
200
N/A
8.74ga17
g.38
3.84
12.88
4,08
N/A
38.27
100
6.06
4.04
12.80
5 2.69
N/A
13.06
collins
200
18.9 g149
5.78
4,90
15.94
15.
3.84
4. 4,42g1m8
N/A
19.49.1.0
50
83.45
28.11
14.57
12.56
22.50
18.07
9,88
NIA
85.41
100
90.73
33.20
15.18:11.0
13.72
29.36
10.77
NIA
91.87 21.22
texture
200
93.31 13.31,11
26.95
18.10
10.39
28.79 1003s
44 44.44
7,30_
NEA
93.78
500
95.61
39.39_9.9
29. 29.60=1.0
13.15
27.70
62.88
10.30
95. 35.06
Average rank
2.91
4.73-a05
6.45
2.48
6.79
4.
8.39go00
g:2l
44

---

Table 26: Classification accuracy (%) of RF, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of specific generator. Different from Table I, "_" denotes generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. failed generators
computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes. TVAE learns the joint distribution p(x, y) and fails to maintain the original training label distribution. TabEBM achieves the best overall performance against Baseline and benchmark generators.
The results of these inapplicable
Datasets
Nwn
SMOTE
TVAE
CTGAN
TaDDDPM
ARF
GOGGLE
TabPPGenn
20
N/A
19.29 .3.ss
13.63
12.71
12.75
20.47
13:25
31.86
34.05 123s
50
56.09_mm
32.29_3.5
19.37
12.62
14.87
32.60
13.29
54.25
56.962138
pretein
100
71.14 Lows
44.50
29.72
12137
1M
34.22
1306
70.68 1304
72.74
200
81.22_231
50. 10
37.08
14.34.315
22.23
43.48
11.76g337
81.93
82.35
500
87.95_1.2
58. 58.172502
49.44
12.03:240
22.88,289
53.674294
10:5945.4
90.81
89. 89.78
20
N/A
11.28
1M.52
9.24
17.76
9.78
31.94
38.16
50
65.32=3a6
N/A
9.98
12.12a2.5
31,7623.66
11.244220
65 65.64-577
66.04-229
fourier
73
44 4<.84_x.
29 2947
11.04
24.
14.60
9.30
74.28 g::
g4.92.3
At most 10 classes
200
78.66_164
48.5 48.56
41 41.942554
10.24-203
31. 11.36.44.0
44.802334
9.884232
79 28:48
79.52.2.0
500
79.64=1.99
$4,80=4a1
57.06.449
11,94
25. 24.0
54.0443.0
10.66:22:
81.64:11:
81.85
69134.613
64.522742
52.83
23.8
80
60.95
50.472967
67.37
67 16
50
70.17
68.14
62.50 1671
54.84
49.94_1a1
67.21
51.99
71.94 14:1
71.91
biodeg
100
74.80
71,8223.0
68.29 2247
56, -5.4
39.62.nss
67.68
50.71
75.68
74.93
200
77.40 -214
22:3.00
69.63 63-63422
35.47
2.53
70.40+3at
48.04458:
78.64=22>
76 76.9622.0
500
80.31
74.83
74.44 12:0
51,30_500
99.68.1.
73.88
45.73
79.56.199
78.66
33:47
55 55.23-431
52. 14444
50,93-629
49.93.106
52.02+5M
48.8844470
$7.20
$8. $8.27=2240
50
62.30_ms4
56.05 56.05_1007
55 24.4
52. 16
49.98
24.55
21.65
64.26
66.98
steel
100
67.63 67.63
58. 58.93
56.664444
51 11.8622552
47 47.84_216
56 1322.99
49. 49.33
72.47 72.47=40:
77.4 77.42.3385
71.41
62. 4444
11.44
48.94 48.94.1.5
58.
28.23
49.25
81.56
86.1 2400
500
77.17
67.4 67:42_115
65, 2117
50, 34.8
49
60.96.144
51 $1.04
86.49 86.49.131
90.60
20
80.81
71.58
48.00 11:4
66.07
61.80 u7.
46.62
84.33
84.65
89.45=2m
74.30-2864
66.754787
19.95
87.73
79.90
41.28-1121
89.27 11:0
20.0
stock
100
91.38=1.0
84.09
79, 16
72.00
90.96:2244
86 38:222
47.7 47.78
92.07
1:35
92. 92.22
200
93.46 (029
86.85_ra2
83.47
78162
17.66
49.91,15..
93.35
11:7
93.07
More than 20 elasses
energy
100
50
N/A
N/A
6.42
4.52,aa2
1.92
4,88 1:
5.40
4.21
1mm
6.62
9.03
3.37
4.47 10:s
N/A
NIA
28.79 1m
39.20
7.12+179
6.01
3.26
11.7845.00
4.32:005
N/A
42.55
100
N/A
6. 10
2.09
11.95
4.95
3.99
NIA
13.67
collins
200
17.74
1.86
4, 4,56
13.22
g.23
4 4.08
N/A
16.24.144
21,18
22.41
10.35
10.55
12:35
19.83
9.50g29)
NIA
100
79.85-202
26. 147
14.842632
15.773511
14, 14.16,442
26.072644
8.9 8.97
NIA
81.99:239
texture
200
84.17
22.70_t.m
12.59 14::
11.61,30
11.68
46.83
10.17
N/A
84.90
500
88.31 133
32.92:
27.62
13.33
10.84,2m
62.04
9.50g534
NIA
85. 14
Average runk
2.55
4.39_mns
210
7:42_
7.09
5.15
8.55
2.36.n0
1.39
45

---

Table 27: Classification accuracy (%) of XGBoost, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. A higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of a specific generator. Different from Table 1, "_" denotes generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. The results of these inapplicable or failed generators are computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes.
TVAE learns the joint distribution p(x. y) and fails to maintain the original training label distribution.
TabEBM achieves the best overall performance against Baseline and benchmark generators.
Datasets
Nus
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
GOGGLE
TaoPFGen
TabEBM
20
N/A
15:47amm
13.60436
15.03
11.77
18.32=
14.61
23 54
25.22
g45s
15
18.88
13.84
12.72
24.39
13.13
16.88
43.79.481
protein
100
25.71
33.23
23 54234
14.964309
14.082144
28.49
14.4
24.91
21.11
200
23.31
35 35.50
26 26.74.s0
15:45:44
14.71=138
36.61
10.41
75 75.20
76.96
41.18
37.95
13.56
14.47
48.92
11.25
11.30
85.39 11 1::0
20
N/A
11.16224
10. 10.3622.55
12.38
14.64-400
9.18
80
26.80
50
41.70
N/A
10.06
10.00
19.96
12.24
43.10
47.16:544
fourier
100
54.52
19:40.441
10.98
12:22
24.24
10.34
40
52.622.50
200
65. 65.96
31.601240
24.76
11,84
13.12
31.74
11.36
14.68
66.26
500
34.72g186
36.561844
11.64
12.72
37.86_134
9.42 16
72.00
74.45
At most 10
66.52
60.3
58.55 25.3
24.65
50.67 4416
20.80
22758
29.5
66.60.2aa7
50
68.01 17
14462
60.53
56. 10
48.13
68.90
$2.89
68. 60
68. 82,
biodeg
100
41.984421
68.71
68
60.67 1000
49.08-3.11
68.74_3.5
49.51 49.51
74.73
72.692436
200
74.29
68.94440
69.87=
19,26
47,26 47,26-119
70.89
53.64 23.6442250
76.03
77.15-253
500
26.04
70.53
73.652354
53.73
47, 2557
74.39
49.08
78.99+2.9
17.61
55.76 u.:0
53.71 13217
51.36
$1.32
51.36
11.1
15 15
46.97
54.38
53.54
16.83
53.60
49.46 19.461457
63.66 03.4446% 53
71.58 114
steel
100
64, 12..1e
59.03+554
57.01
$2.864306
44, 22.7
58.21
46 92
88.61
96.34_277
24.4
58.421ate
59.25 39.25
51,94
43,96 1094
58.92
19.58
28.85
99. 20.72
500
61.11 to
65.70
51.68
46.63
39.19
49.98
99.62
99.92.s0
20
77, 25.
64.61
50.93
67. 2134
14.63-11A4
68, 28
45.59
80. 14:444455
84.22
stock
100
87 21
80. 80.12
13757.1576 17.8
77 23:433
71.05 :1.03:30s
1608
85.72.400
44
83.91 =319
79.19
55
11
20
86.97 1:25
89 29.21
91.14
200
90.58 1110
83.34
11.04
76.60,..
91.52
.7.49.341
55,43
90.78
90.94_110
7.37
5.16
1.90
3.95
6.62
19.38_
More than 10 classes
energy
100
NIA
8. 8.25
5. 5.40
3.95
10.21
NIA
N/A
25.008
200
697,
8.56
1.21
11.08,7
N/A
N/A
31,03-191
collins
200
100
12.52
N/A
5.52.11.7
4.45 10ns
4.43g06
3.98 jom
g.18
9,06
5.39 L.
5.61
NIA
NIA
N/A
N/A
11.49:145
9.03 11
2:59
20.94
9,44
12.63
11.32
14.35
N/A
68.97
100
69. (0,80,..
13
14.06.449
16.18
9,90
19.13
NIA
NIA
76.62
texture
200
78 78.464222
23.324704
15.094296
15. 15.15
9.06
33.67=500
NIA
N/A
S0.37
86.392130
31.134915
22.88
13.464577
10.22
47.06
Average rank
2, 2.76xa30
4.97
6.39 6.39.1.22
7:42au2s
7:48.138
4.97
7.11
2.6240s5
1.27
46

---

Table 28: Classification accuracy (%) of TabPEN, comparing data sharing on eight real-world tabular datasets with varied real data availability. We report the mean + std balanced accuracy and average accuracy rank across datasets. higher rank implies higher accuracy. Note that "N/A" denotes the inapplicability of a specific generator. Different from Table I, "-" denotes a generator cannot satisfy the requirement of generating 500 stratified samples even after generating 10,000 synthetic samples. The results of these inapplicable or failed generators are computed with the mean results of other methods. We bold the highest result for each dataset of different sample sizes. TVAE learns the joint distribution p( x, y) and fails to maintain the original training label distribution. TabEBM achieves the best overall performance against Baseline and benchmark generators.
Datusets
Nea
SMOTE
TVAE
CTGAN
NELOW
TahDDPM
ARF
GOGGLE
TabPFGen
TabEBM
20
N/A
16.36_139
13:22
14.80
12.93
12.55
12.14_116
33.46.556
24.50
50
59.60
27.5 27,51=122
18 18:26:4444
13,28
14.95a152
29 29.824831
13,30_138
57 37.684210
59 59.00
protein
49.47
41.49=608
50.50
13.69
17.21
36.73
12.61-0a1
78.93
79.024574
200
90. 90.49.221
48,30 48.30
36 36.99
13.71
21.67=332
43.53
12,96-1.
91.47.1.5
90.7 a1.31
94. 28.36
58.3 12.3
48.524470
12.91
23.35g1.6
57.374525
12.51
95.26
95.00
20
N/A
13.98 Line
10.64
10.56
16.44
10.56 1,.0
29.42 1.
36.56 1:95
50
52.52
N/A
10.24
10.72:1.55
27.824541
9,90-
53.98
$3.92
fourier
63.36
28
10.30_1.1
11.84
30.76
10.32 1m0
65 65.32,170
65.58 1:
At most 10 clanee
200
69. 62 14m
40.36
40.08 1517
8.82 8.82
32,98
38.50
10.30
72.08
72.26,220
500
75. 24.14
46.56_1M
g4.38
9.52
32.46.4m
49.62.
10.68_1.4
75.98
75.60
20
69.00 09.011.0
65,35
52.29
s0.00.cm
57.11
50.35 1111
70.77
71.36,510
50
73.27 +3.3)
68.69
63.31
$4.85
50.00
71.23
50.00_oo0
75.78
75.56
biodeg
36.39 13
73.06.4m
7175
55.262651
50.00..mm
73.02,aa45
50.00_.o
200
80. 80.52.055
73, 13.19
72.93
$4,942851
49 23.3
76.03-2255
50.00_o0
82. 82.22
82.70 82.70
82.47
77.06_103
19.18
50.47
49.67
77.79
50.00_0o0
83.03
83.67
20
56 g
53,88 2308
52. 12
50.00
50.47
50.00-toa
64 64.922475
65.82.sn.9
50
62.4 62.45
$7.80 2718
57. 11
51.84
50.00
56 40
50.00_6o0
84.81
866.22.4.55
71.25 sate
2404
50.59
48.48
55.74 $5.74
50 50.66
07.29:. 97.29.1140
97.85 11.30
200
77. 96.96633
63,9 23.9221333
64 64.224457
50.00=uae
47.65
02.33
50.00-com
98 28
98.89 20.9
500
85,29
69.41
13.34
50.09.uu3
50.00.cm
68.7815M
50.00
99.71
99.71
20
83.79 1::00
70:4
70.75 mes
78.58 18.58
66.66
51,45 4v0
82.98 14:47
83.7 $3.79..490 14.96
50
89.91
17.18
70.04
72.42.8.57
89.35
78.06
50.00 50.00_.om
89.97
911,17 911
stock
92.05 11.34
81.60_3m
78.73
75.24
91.32
15.2412w
92.25 11:11
92.46 11:3
200
93.50.mn
85,46 85.46g301
83.47.30
75.51
92.95g104
87.25
50.00_om
93.93
93.65
Averuge rank
2.77
4.73
5.88 56
7.42
g.
g.21
8.42_om
1.85
1.40
47

---

D.7.2 DCR Evaluation
Table 29; DCR between real train data and synthetic data on eight real-world tabular datasets with varied real data availability, We report the mean = std result and average rank across datasets. A higher rank implies better privacy preservation. Note that "N/A" denotes that specific generator was not applicable, and the rank is computed with the mean result of other methods. We bold the highest result for each dataset of different sample sizes. Even though ARF and NFLOW show high DCR, our experiments demonstrate that they do not learn the data distribution well, leading to poor downstream accuracy. TabEBM achieves competitive overall DCR against benchmark generators.
Dutascts
Nia
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
TabPFGen
TabEBM
20
N/A
0.24
0.36
0.29
0.60
0.49
0.24
0.39
50
0.20
0.34
0.42-006
0.21
0.62
0.47
0.21
0.37
protein
100
0.20
0.33
0.37_005
0.26
0.54
0. 0.4610.06
0. 0.12
0.27
200
+.19s
+00s
0.35_a00
2004
0.44
0. 0.
0.26
500
0.
100.0
0.32
0.30
0.33
0.48 L003
1.43
0.09 10.05
0.23 10.13
20
N/A
0.19
0.61-004
0.52-20.08
0.56:0005
0.57
0.48
0.40
50
0 40a2
0.29
0.48 0.48-0.1
0.33
0.67=00s
0.54 0.54
0.31
0.43
fourier
100
1.202
10.0
0.50
0.00
1..09
0.60 1000
0.59 10.05
0.31 10.07
0.44
At most 10 classes
200
4.202
0.56
0.53
_.03
0.37
0.58
0.56
0.30
0.46
500
0.25
0.67
0.54_000 06
0.40
0.62-004
0.61 10.05
0.28
0.45 20.05
20
0.2
0.19+no8 0.29
0,26_007
0.33
0.26-a15
0.46:0.05
0.38
0.39
50
0.
1.100
0. 0.17
0.16-004
0.24
0. 0.14
0.31 20.05
0.31 10.07
0.30
biodeg
100
0.11 10.04
0.17:1044
0.17-0004 04
0.22
0.10=z02
0,21 10.02
0.24
0.21 20.05
200
0.08
0.14+0..2
0.14-000
0.20
0.11 =004
0.20 +0,04
0.13
0.15 +0.0
500
0.16+
0.13_008 03
0. 1800.5
0.10
0.18 20.3
0.05
+0.94
20
0.38
20.30
0.25 _0112
0.33
0.48_
0.43
0.23
0.21 4o.us
10.11
0.27
0.22 0.09
0.34
0.45
1.401
0.15
0.24
steel
100
0.20
0.28++0.7
0.22-0.8
08
0.30
0
0.41
+0.07
0.15
0.25
200
0.
0.19
1..0s
20.8
0.22
0.32.
0.31 0.11
0.40
0.14
0.30
500
0.1 1..00
0.29
0.24_
0.32.
0.21
0.37
0.10
0.25
20
0.24
0.37
0.42-007
0.46
0.50 0.45
00.1
0.46
50
0.40
0.34_004 04
0.43
0.28
0.39 +0.03
0.37
0.46 0.46
stock
100
0.15
0.39
0.33 0.33_aus
0.46
0.17
0.33 2o:3
0.34
0..4
200
0.38 0. 10.02
0.28 0,28_o03
0.45 10.05
0.11 0.11
0.32
0.39
0.46
More than 10 classes
50
N/A
10:20
0.36 0.08
0.48 10.07
0.46 0.00
N/A
0.44
energy
100
N/A
0.08 10.17
0.40
0.46 20.6
0.00
0.40
N/A
0.40
200
N/A
0.04
0.30
0.45 0.45
0.00
0.38 0.38
N/A
0.42
100
N/A
0.30 0.00
0.33
0.26
0.33
N/A
0.38
collins
200
0.18
0.00
0.23_006 06
0.29
0.192003
0.33
N/A
0.36
50
0.21
0.00
0.17-a.19
0.26
0.26
0.42
N/A
0.40
100
0. 164040
0.08
0.35_on6
0.26gnas
0.46 0.37
N/A
0.42+a.10
texture
200
0.24 0.13
0.29 2.12
0.32
0.40_aox
0.37
N/A
0.42
500
1.032
0.04
0.15_o 11
0.34
0.37
10.03
N/A
0.44
Average rank
6.64
5.48 12.08
4.82 1.42
3.45 11.75
4.03 222
2.21 2.2111.17
11.5
1.52
48

---

D.7.3 Delta-presence Evaluation
Table 30: 5-presence between real train data and synthetic data on eight real-worid tabular datasets with varied real data availability. We report the mean std result and average rank across datasets. A higher rank implies better privacy preservation. Note that "N/A" denotes that a specific generator was not applicable, and the rank computed with the mean result of other methods. We bold the best result for each dataset of different sample sizes. TabEBM achieves the best overall
performance against benchmark generators.
Datasets
Naai
SMOTE
TVAE
CTGAN
NFLOW
TabDDPM
ARF
TabPFGen
TabEBM
20
N/A
1.03
1.33
0.13
0.07
0.05 1004
0.031000
0.03
50
0.07 2000
0.07
0.07
0.39_a92
2.
0.09
0.07
0.07 0.07
protein
100
0.19
0.36
0.50
2.45-333
0.23
0,36
0.17
0.17
200
0.62
2.84
2.03
11.55=7744
1.71
2.73
0.17
0.57
500
1.15
1011
1.62
2.41
26.85_999
6.51
2.26
1.20
1.20
20
N/A
0.02+0000
0,02
0.06=a07
0.04
0.04
0.02++0000
0.02-
50
0.08 1000
0.09 0.1010001
0.09
0.08 10000
0.08 10.00
0.08 10.00
0.08 10.00
fourier
100
0.18
0.11
0.26
2.74
0.30
0.53
1.17
0.17 10001
Armast 10 clasves
200
0.73
1.56
3.52
10.60
1.52
2.52-21.4
0.45
0,44
500
1.42
6,06
5.65
22.53
3.39
2.99
1. 1.18
1. 1.16
20 0,03
0.12+0.15
0.22-2032
0.03
0.14
0.03-2000
0.03
50
0.08 20001
0.10
0.08
0.12
0,10
0.10.00.0
0.08 g000
0.08
biodeg
100
0.35 20
0,52+029
0,98
1.14_a89
0.59
0,51 =0.30
0.2 0.24
0.24
200
2.35
1176
2.27
2.80
4.18 1174
4.144
1.70.10.2
1..4
10:25
500
2.91
21
3.95
3.58
8.85 8.85_g307
11.9228. 19
2.
1.57 10.4::0.0
20.42
20
10.1
0.1010.12 1.08s
0.08 .0.06
0.06
0.15
0.03
10.00
0.03 10.00
50
0.08 2008
0.12
0.09
0.17-008
1.04
0.09
20.00
0.08 20.01
steel
100
0.22
2.3
0.44
0.73-0030
2.17
0.27 10.06
0.20
:000
0 0.20=
200
1.39
2.05
3.39
5.55
6,68
1.29
0.49 +0007
0,48
500
1.43
1.39
1.23
10.52_1.2
33.92 25.31
2.39 10.38
1,68 10.88
1.70_o.
20
0.03
0.03
0.00
0.03_aom
0.04
0.03
0.03
0.03
50
0.08 10.00
0.09 1.09
0.08 0.08_.o0
0.09
0.08 10.00
0.08 10:00
0,08 10.00
stock
100
0. 10002
0.23
0.26
0.23
0,22
0.20
0. 11000
0.18 10.01
200
0.51
0.97
1.83
0.90=a032
0.57
0.60
0. 0.49
0.48 08
More than 10 classes
50
N/A 0.09
0.08
0.08_am
0,06
0.08
N/A
0.08
energy
100
NIA
1.56
0.19
0.19
0.99
0 0.16
N/A
0.16
200
NIA
4.15
1.67 26.7
0.72
13,28
0 2.44
N/A
0.38 20.8
100
N/A
0.18 1.79
0.18 Loos
0.17 0.17
N/A
0.16
collins
200
0.43
2008
4.20
0.76
1.73
0.94
0.95
N/A
0.39 20.05
50
0.08 1000
1.08
0.08 10.0
0.08 _,08
0,10
0.08 10.0
N/A
0.08
100
0. 1001
0.421022
0. 0.19
0.41-
0.44
0.25
N/A
0.17 10.01
0.17
texture
200
1.
2.34
1.762105
5.78-282
7,02
1.54
N/A
0.45
20.08
500
2.88
2.42+135
23.40
16.64_12235
2.36
N/A
1.03 1003
Average rank
3.30
1.91
5.30
6.45 6.85_1.86
5.82
4.45 11.6
3.00
49

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: Section details our research objectives and highlights our contributions.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: Presented in Section
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: Section presents the theoretical results of our proposed method.
4. Experimental Result Reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: Refer to Appendix B, where we provide full details on reproducing the results in the paper. We provide an open-source library of the proposed method.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification: Refer to Appendix B. All datasets used in this paper are publicly available, and the implementations of benchmark generators open-source. We also provide open-source library https: //ggt/ubttttttttg com/ andreiimargeloou/TTab.MM
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: Appendix B provides full descriptions of the experimental setup.
7. Experiment Statistical Significance
Question: Does the report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: Refer to Section 3, where we provide standard deviations for all tables. Figure 6 and Figure 4 (Right) contain error bars. Due the page limit, the error bars for all other figures are available in Appendix D. In Section 3.2 and Appendix D.6, we show statistical significance tests of the similarity between real data and synthetic data.
8. Experiments Compute Resources
Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
50

---

Answer:
[Yes]
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51


Reviews:
[{"review_id": "Gf4T4Re70Q", "reviewer": "Reviewer_tdoQ", "summary": "The paper introduces TabEBM, a class-conditional generative method for tabular data augmentation using distinct EBMs for each class. By modeling each class's data distribution individually, TabEBM generates high-quality synthetic data. Experiments demonstrate that using TabEBM for data augmentation improves classification performance across various datasets, particularly small ones.", "questions": "1. Do the datasets used in the experiments only contain continuous features and no categorical features?\n2. The TabEBM method is similar to TabPFGen [48]. Why didn't you use the 18 datasets mentioned in the TabPFGen paper for experiments, but instead chose 6 different datasets (with a smaller test scope) for evaluation?", "limitations": "N/A", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper introduces distinct class-specific EBMs for tabular data augmentation. Moreover, it presents thorough experiments demonstrating effectiveness across various datasets, especially small ones. Additionally, the writing is well-structured and clear.", "weaknesses": "1. On the technical level, TabPFN, EBMs, and SGLD have all been introduced in TabPFGen [48]. The main difference in the proposed TabEBM method is the use of class-specific EBMs. However, this idea is straightforward and lacks novelty.\n2. The most significant difference between tabular tasks and common tasks like images is that they include both continuous and categorical features. However, TabEBM treats all features as continuous, lacking targeted consideration for categorical features.\n3. In TabEBM, although the choice of surrogate binary classifier is arbitrary, not using training-free models like TabPFN will result in training costs being positively correlated with the number of classes, significantly increasing the training overhead.\n4. The datasets used in the experiments have a maximum dimensionality of 77, lacking experimental results on high-dimensional data (e.g., hundreds of dimensions).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful review! We address **all** of your questions and comments below. Due to space constraints, we summarised the new results. We will update the manuscript to include the complete new experiments and clarifications.\n\n## >Q1/W2: Do the datasets contain categorical features? How does TabEBM handle them?\nYes, we evaluated TabEBM on datasets containing both continuous and categorical features. Specifically, Table `R1` shows the two considered datasets with mixed feature types. In lines 639-640, we also clarify that TabEBM encodes the categorical features with leave-one-out target statistics. As the reviewer mentioned, the evaluation results (Table 1) show that TabEBM is effective across various datasets, including those containing categorical features.\n\n*Table `R1`.* Number of categorical features in the datasets considered.\n|Dataset|#Categorical|\n|---|---|\n|**Main text**||\n|protein|4|\n|energy|1|\n|**New datasets in our response to Q2**||\n|support2|7|\n|mushroom|22|\n|abalone|1|\n|statlog|13|\n## >Q2: Why not evaluate the 18 datasets in the TabPFGen paper?\n**Firstly,** we wanted to avoid data leakage and ensure a robust comparison by also evaluating datasets not in TabPFN's meta-test (Appendix F.3 in its original paper). As the 18 datasets in the TabPFGen paper were all used for constructing and evaluating TabPFN, we also use different, leakage-free datasets. **Secondly,** our test scope is not smaller than that of the TabPFGen paper. We evaluate a wide range of test scopes, considering different datasets and varying the availability of real data. We also include datasets with categorical data, unlike TabPFGen, which investigates only numerical features. Our setup (i.e., eight datasets × five sample sizes) leads up to 33 different test cases. For reference, ARF has the most test cases among prior studies, with 20 test cases, while TabPFGen follows with 18 test cases. **Thirdly,** we further provide **new results** on six more leakage-free datasets for UCI with 7-42 features, some including categorical features. We set $N_\\text{real}=100$ and provide results for the Top-5 benchmark methods. Table `R2` shows that TabEBM continues to outperform all other benchmark methods.\n\n*Table `R2`.* Classification accuracy (%) comparing data augmentation on six *new* leakage-free datasets.\n|Datasets|Baseline|SMOTE|TVAE|CTGAN|TabDDPM|TabPFGen|TabEBM (Ours)|\n|---|---|---|---|---|---|---|---|\n|clinical|68.63|71.07|61.80|65.21|54.03|69.66|**71.20**|\n|support2|64.23|65.60|60.70|59.14|58.31|64.34|**65.28**|\n|mushroom|95.51|95.84|93.75|93.26|79.87|**97.05**|96.82|\n|auction|51.90|57.35|53.09|52.35|51.14|56.82|**57.97**|\n|abalone|11.59|N/A|8.49|7.72|9.95|N/A|**13.56**|\n|statlog|56.22|57.30|53.12|55.55|53.07|57.65|**57.85**|\n\n## >W1: The core ideas “have all been introduced in TabPFGen” … \"this idea is straightforward and lacks novelty”\nTabEBM makes a novel contribution to the field of tabular data augmentation by being the first to introduce class-specific generators, as we discussed in our related work, as well as acknowledged by all other reviewers.\n\nSpecifically, TabEBM is the first method to create distinct class-specific EBMs. It consists of individual models—one for each class—designed to learn distinct marginal distributions for the inputs associated with each class. TabEBM's *class-specific generation* is not available to TabPFGen, and it is only possible due to our proposed *surrogate binary tasks*, which enable the creation of a binary classification task for each class and the obtaining of the class-specific EBM via Equation 3. The results demonstrate that training class-specific EBMs significantly improves the inferred energy over TabPFGen under high levels of noise (Figure 7) and high data imbalance (Figure 8). Unlike TabPFGen, which supports only 10 classes, TabEBM can handle an unlimited number of classes. As you rightly point out, our extensive experiments demonstrate that our method, with its class-specific generation, outperforms all other methods in accuracy, statistical fidelity, and privacy.\n\nIn addition to the method, our paper makes two additional key contributions. First, we conduct the first extensive analysis of tabular data augmentation across various dataset sizes. Our benchmark reveals that existing tabular augmentation methods may improve performance only on small datasets, a previously uninvestigated issue. Second, we will release our method as an open-source library for tabular data augmentation, allowing users to generate data immediately without additional training.\n\n## >W3: “In TabEBM … not using training-free models like TabPFN will result in … significantly increasing the training overhead.”\nBecause we tackle classification problems on *small-size* datasets, training models from scratch is not practical, often leading to suboptimal performance due to overfitting. Instead, using pre-trained models, such as TabPFN, is integral to our approach. From a practical standpoint, using pre-trained models makes TabEBM immediately usable. A significant limitation of existing tabular generators is their need for training, which can be time-consuming, error-prone, and typically requires GPUs. In contrast, our TabEBM library (included with the submission) allows users to start generating data immediately without additional training or tuning. \n## >W4: Lacking experimental results on high-dimensional data\nAs noted in Lines 317-323, scaling up in-context tabular models for high-dimensional data remains an unresolved challenge and is not the primary focus of our study. Instead, TabEBM is designed to demonstrate the effectiveness of using pretrained in-context tabular classifiers for generating tabular data. As acknowledged by the reviewer, and further shown in our response to Q2, our \"thorough experiments\" demonstrate TabEBM's effectiveness.\n\nThank you again for your thoughtful review! We would appreciate it if you would consider raising your score in light of our response.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "vgUIpos5U3", "reviewer": "Reviewer_Cc3y", "summary": "The authors present a new method of tabular data augmentation, called TabEBM. The unique feature of TabEBM is that it creates distinct generative models for each class in a classification problem setting. With extensive and thorough evaluations, the authors prove that TabEBM sets the new state of the art.", "questions": "1. The definition of a surrogate binary classification task (lines 111-113) might result in class imbalance. How is this potential problem addressed? \n2. Can the authors provide more details on training the models for the surrogate binary classification task?  This could eliminate some other questions.\n3. Have the authors specifically investigated the propensity of TabEBM to generate outliers? How does TabEBM compare to other methods in this regard?\n4. In section 3.2, the authors describe many statistical evaluations performed. However, the multiple hypothesis testing aspect is not described in sufficient detail. How were the p-values adjusted? How strong is the impact of a particular correction method on the final results (tables of C3)?\n5. Can the authors share more insights about the open-source library? This is positioned as one of the key contributions, but the code is not provided and the practical considerations of using the library are not clear from the submission.", "limitations": "Briefly discussed in section 4.", "rating": 7, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. The manuscript is well organized. The text is clear. The quality of the figures is high. \n2. The authors address a very common problem for the broad scientific community. Application of machine learning algorithms on small tabular datasets is limited by design. Introducing TabEBM as an effective data augmentation method, this work can have an extremely broad impact in the future.\n3. The experiments are rich and rigorous. The method is compared against many existing methods on a variety of datasets. The evidence proving its effectiveness is convincing.\n4. The authors claim TabEBM will be available as an open-source library.", "weaknesses": "Some important details on study design, model training, and practical considerations of TabEBM application are missing. See questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful review! We address **all** of your questions and comments below. Due to space constraints, we summarised the new results. We will update the manuscript to include the complete new experiments and clarifications.\n\n## >Q2: Provide details on training models for the proposed surrogate binary classification tasks\nIn TabEBM, for each class $c$, we train a class-specific EBM, $E_c(x)$, using exclusively the data from that class, denoted as $\\mathcal{X}_c$. The energy function $E_c(x)$ is derived by adapting the logits from a binary classifier, as outlined in Equation 3. To train this classifier with only class-specific data, we create surrogate binary classification tasks.\n\nOur surrogate classification tasks determine if a sample belongs to class $c$ by comparing $\\mathcal{X}_c$ against a set of \"negative samples,\" $\\mathcal{X}_c^{\\text{neg}}$. We intentionally create these negative samples at a distance of five standard deviations from the original data to ensure the binary classifier can easily differentiate between the real class data and these artificially distant samples.\n\nWe label the true class samples $\\mathcal{X}_c$ as 1 and the negative samples $\\mathcal{X}_c^{\\text{neg}}$ as 0, forming a combined dataset $\\mathcal{D}_c = (\\mathcal{X}_c \\cup \\mathcal{X}_c^{\\text{neg}}, \\{1\\}^{|\\mathcal{X}_c|} \\cup \\{0\\}^{|\\mathcal{X}_c^{\\text{neg}}|})$. Following this, we train the TabPFN classifier on $\\mathcal{D}_c$, resulting in a binary classifier specific to class $c$. This classifier is then used to define the energy function $E_c(x)$ using Equation 3, from which we can generate data using SGLD.\n\n## >Q1: Does the surrogate binary classification task result in class imbalance issues?\nNo, the imbalance between the \"negative samples\" and the real samples used in the surrogate binary classification task has a negligible impact on TabEBM's performance.\n\nWe conducted a new experiment to evaluate the effects of varying the ratio $\\|\\mathcal{X}^{\\text{neg}}_c\\|:\\|\\mathcal{X}_c\\|$. To ensure reliable outcomes, we maintained a consistent ratio across all classes, keeping the same proportion of negative samples for each class. We varied the number of negative samples $\\|\\mathcal{X}^{\\text{neg}}_c\\|$ to represent various ratios of $\\|\\mathcal{X}_c\\|$, thus simulating both balanced and highly imbalanced scenarios. \n\nThe results, presented in Table `R3`, computed across six datasets with $N_{\\text{real}} = 100$ real samples, demonstrate that TabEBM is robust to potential imbalances in the surrogate binary tasks.\n\n*Table `R3`.* Classification accuracy (%) on data augmentation, showing the impact of the number of negative samples $\\|\\mathcal{X}^{\\text{neg}}_c\\|$ in TabEBM across six datasets. TabEBM's performance is robust regarding the number of negative samples.\n|Ratio$\\|\\mathcal{X}^{\\text{neg}}_c\\|:\\|\\mathcal{X}_c\\|$|`1`|`0.5`|`0.2`|`0.1`|Fixed$\\|\\mathcal{X}^{\\text{neg}}_c\\|=4$|\n|---|---|---|---|---|---|\n|Average accuracy improvments|+2.91|+2.87|+2.88|+2.92|+2.90|\n\n## >Q3: TabEBM's propensity to generate outliers\nWe provide fair and thorough comparisons by (i) including a wide range of evaluation metrics and (ii) utilising a large synthetic set (Lines 183-184). Given our extensive test scope (i.e., eight datasets $\\times$ five sample sizes), it is computationally infeasible to employ complex and specialised methods to detect outliers in synthetic data. However, the downstream accuracy and statistical fidelity metrics are highly indicative of the distribution shifts between real and synthetic data. Notably, Figure 3 illustrates that TabEBM consistently outperforms the baseline across various sample sizes and class numbers. We believe these two metrics adequately demonstrate that TabEBM is more stable to generate in-distribution samples than benchmark methods.\n\n## >Q4: Details on the multiple hypothesis testing in Section 3.2\nWe aim to provide a fair and coherent comparison between TabEBM and existing methods, and thus, we follow the widely-adopted evaluation process in prior studies. Specifically, we compute the statistical fidelity metrics with the open-source implementations from the well-established open-source library Synthcity. However, the previous studies often operate under the assumption that the issues associated with multiple comparisons are less pronounced in generating low-dimensional tabular data, hence correction methods for multiple hypothesis testing are seldom employed. We will further clarify this in the revised manuscript.\n\n## >Q5: The code for the open-source library is not provided\nWe included the TabEBM library as a zip file in the Supplementary material. The library has two core functionalities:\n\n1. *Generate synthetic data*: The library can generate data that can be used as additional training material for data augmentation. We have included a demo notebook, `TabEBM_generate_data.ipynb`, in the attached codebase. This notebook demonstrates how to use the generated data for data augmentation and shows a toy example comparing the quality and position of the synthetic data with the real data.\n\n```python\nfrom TabEBM import TabEBM\n\ntabebm = TabEBM()\naugmented_data = tabebm.generate(X_train, y_train, num_samples=100)\n# augmented_data[class_id] = generated data for a specific `class_id`\n```\n\n2. *Compute & visualise the energy function*: We allow users to compute TabEBM's energy function and the unnormalised data density. The demo notebook, `TabEBM_approximated_density.ipynb`, shows TabEBM's energy under conditions of data noise and class imbalance.\n\nWe will make the TabEBM library freely available after publication. It is easy to use, domain-agnostic, and requires no training, making it suitable for data augmentation, especially for small-sized datasets.\n\n\nThank you again for your thoughtful review! We would appreciate it if you would consider raising your score in light of our response.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "Ok2z5XZUdP", "reviewer": "Reviewer_iojh", "summary": "The paper proposes TabEBM, a novel data augmentation method designed for low-sample-size tabular classification tasks. TabEBM generates synthetic tabular data using class-specific Energy-Based Models (EBMs) to learn the marginal distribution for each class. Experimental results on various real-world datasets demonstrate that TabEBM improves downstream performance via data augmentation, generates high-fidelity synthetic data, and strikes a competitive balance between accuracy and privacy in data sharing.", "questions": "- How does TabEBM perform on datasets with  hundreds of features?\n- Could the approach be extended to use other pre-trained models besides TabPFN?\n- How does the method handle highly imbalanced datasets where some classes have significantly fewer samples than others?\n- What is the computational complexity of generating samples compared to other methods?\n- How sensitive is the performance to the choice of hyperparameters in the SGLD sampling process?\n- Clarify the meaning of the word \"fit\" which is used in line 122 of the paper.", "limitations": "- Performance may degrade for datasets much larger than those tested.\n- Inherits limitations of the underlying TabPFN model.\n- May not be suitable for datasets with extremely high dimensionality.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Novel approach using class-specific EBMs for tabular data generation.\n- Comprehensive evaluation across multiple datasets, metrics, and downstream tasks.\n- Strong performance, especially in low data regimes.\n- Thorough analysis of statistical fidelity and privacy preservation.\n- Open-source implementation provided.", "weaknesses": "- Scalability Issues: The reliance on TabPFN, which struggles with large sample sizes, limits TabEBM's scalability.\n- Implementation Complexity: The need for class-specific surrogate tasks and the iterative nature of the sampling process may complicate implementation and increase computational overhead.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful review! We address **all** your questions and comments below. Due to limited space, we summarised the new results. We will update the manuscript to include the complete new experiments and clarifications.\n\n## >Q3: How does TabEBM perform on highly imbalanced datasets?\nWe conducted **new experiments**, adjusting the class imbalance on two binary datasets (with $N_\\text{real}=100$). We keep the setup from Section 3 and report the balanced accuracy averaged over six downstream predictors. Table `R4` shows that under high class imbalanced, TabEBM outperforms the Baseline and SMOTE, which is a method specifically designed to handle imbalanced datasets.\n\n*Table `R4`.* Test balanced classification accuracy (%) varying the class imbalance.\n|**Datasets**|`(#Minority:#Majority)`|Baseline|SMOTE|TabEBM(Ours)|\n|---|---|---|---|---|\n|**steel**|`(50:50)`|88.79|77.74|**93.77**|\n| |`(10:90)`|60.74|60.76|**73.02**|\n| |`(5:95)`|52.29|56.11|**65.95**|\n|**stock**|`(50:50)`|88.64|**90.21**|90.16|\n| |`(10:90)`|76.05|83.86|**84.92**|\n| |`(5:95)`|65.98|75.24|**77.68**|\n\n## >Q5: How sensitive is TabEBM to the hyperparameters of the SGLD sampling?\nWe run **new experiments** varying two key hyperparameters of SGLD on the “biodeg” dataset with $N_{\\text{real}}=100$. Specifically, we vary the step size $\\alpha_{\\text{step}}$ and the noise scale $\\alpha_{\\text{noise}}$, reporting the accuracy averaged over six downstream predictors.\n\nTable `R5` shows that TabEBM is stable to these hyperparameters, as the difference between the highest and lowest accuracy is less than 1.5%. Note that increasing $\\alpha_{\\text{noise}}$ (which is added at each SGLD step) is expected to degrade performance because we standardized the data to have unit standard deviation.\n\n*Table `R5`.* Classification accuracy (%) of TabEBM with different SGLD settings\n|$\\alpha_{\\text{step}}\\rightarrow$|0.1|0.3|0.5|1.0|\n|---|---|---|---|---|\n|$\\alpha_{\\text{noise}}\\downarrow$| | | | |\n|0.01|76.45|77.09|77.04|76.58|\n|0.02|76.86|76.96|76.77|76.26|\n|0.05|75.93|75.89|75.94|75.70|\n\n## >Q6: Clarify the meaning of the word \"fit\" on line 122\nWe use the term “fit” to mean “train” the in-context model TabPFN. For TabPFN, “training” is similar to the K Nearest Neighbour algorithm, where \"training\" means defining the training dataset used for inference. Thus, we simply update TabPFN's training datasets and the model in inference mode, thus never updating its parameters.\n\n## >Q4: How does TabEBM's computational complexity compare to other methods?\nFigure 4 from the paper illustrates the trade-off between accuracy and the time required for training and generating 500 synthetic samples. The results show that TabEBM is the fastest method for generating data besides SMOTE. Other methods are 3-30 times slower than TabEBM. Also, TabEBM surpasses all other methods in improving downstream accuracy through data augmentation.\n\n## >W2: Class-specific surrogate tasks and iterative sampling can complicate implementation and increase computational overhead\n**On implementation complexity**: TabEBM simplifies implementation by eliminating the need for dedicated training, pipelines, protocols, and resources—making it ready to use for generating data. We provide an open-source implementation of TabEBM, allowing users to generate data with just two lines of code for new datasets. We believe this ease of use will encourage the widespread application of tabular data augmentation on small datasets.\n\n**On the computational overhead**: As mentioned in our answer to Q4 and Figure 4, TabEBM is computationally efficient, being the fastest method for generating data besides SMOTE —while outperforming all competing methods.\n\n## >Q2: Can TabEBM use other pre-trained models besides TabPFN?\nYes, TabEBM can be used with other pre-trained models besides TabPFN. In the paper, we use TabPFN because it is the only tabular model of this type with open-sourced weights. However, TabEBM is a general method for transforming classifiers into class-specific generators and can use any gradient-based in-context classifier that computes logits (through Equation 3). As new tabular foundational models are developed `[1]`, they can be readily integrated into TabEBM.\n\n## >Q1/W1/L1/L2/L3: On the scalability and limitations of TabEBM\nTabEBM is a method that uses an underlying binary classifier, thus its capabilities and limitations are directly influenced by the in-context model it employs (TabPFN in our case), as discussed in the paper (Lines 317-323). Since TabPFN handles only up to 100 features, this limitation is also inherited by TabEBM.\n\nOur **new experiment** (Table `R6`) shows that TabEBM can be applied to larger datasets beyond TabPFN's limitation of 1000 samples. On larger datasets TabEBM still outperforms other generators (not shown due to space limits), but training on real data alone appears sufficient. This highlights TabEBM's usefulness in fields with limited training samples. Note that despite TabPFN's 10-class limit, TabEBM can handle unlimited classes by using TabPFN only for surrogate binary tasks.\n\nAs foundational models for tabular data evolve `[1]`, new models that can accommodate more features are anticipated. Integrating these models into the TabEBM framework will enable it to handle high-dimensional datasets, thus increasing its versatility and utility.\n\n*Table `R6`.* Classification accuracy (%) comparing data augmentation with increased real data availability on the “texture” dataset\n|$N_{\\text{real}}$|Baseline|Improvement by TabEBM (%)|\n|---|---|---|\n|50|72.40|+6.50|\n|100|82.42|+3.59|\n|1000|96.37|-0.07|\n|2000|97.76|+0.07|\n|3000|98.20|+0.15|\n|4000|98.51|+0.04|\n\nThank you again for your thoughtful review! We would appreciate it if you would consider raising your score in light of our response.\n\n**References:**\n- `[1]` Boris van Breugel, Mihaela van der Schaar, *Why Tabular Foundation Models Should Be a Research Priority*, ICML 2024 (https://arxiv.org/abs/2405.01147)", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "DqurcGisJU", "reviewer": "Reviewer_XdB4", "summary": "The authors address the problem of data augmentation for classification tasks by proposing a novel approach that utilizes separate energy-based models (EBMs) to generate synthetic data for each class. These EBMs are derived directly from the logits of a binary classifier whose goal is to distinguish real data from negative data. These logits (their logsumexp over positive and negative classes) are reinterpreted them as an energy function for each class.\nIn order to avoid training these classifiers on the data itself, the authors take advantage of a pre-trained Prior-Data Fitted Network (PFN).\n\nThe authors perform a comprehensive evaluation of their method comparing it to competing methods for data augmentation on a number of small real world datasets. They show that their method is the only one that offers a consistent improvement in classification from the addition of synthetic data.", "questions": "- Can you provide a convincing explanation for why the logits from discriminative classifiers derived from TabPFN should be useful when reinterpreted as a class-conditional energy function in light of the first point above? Without a clear justification, it is difficult to understand the basis for expecting this method to work effectively.\n\n- Since the authors marginalize over $y$ by taking the LogSumExp over the $y=0$ and $y=1$ logits corresponding to negative and empirical class data, respectively, one would expect the energy function to represent a mixture distribution between these two densities. Why aren't the logits for $y=1$ used directly as an energy function instead? In other words, what is the motivation for marginalizing over $y$ when it is simply an indicator of whether the data is real or negative?\n\n- The details of how the negative examples are generated are not clear. The text simply states: \n\"These surrogate negative samples $\\mathcal{X}^{neg}_c$ are constructed to be far from the distribution of real data, ensuring that the classifier can easily distinguish them. This placement prevents class ambiguity and facilitates a robust energy landscape\". The appendix does provide some additional details, but it is still ambiguous how this data is generated. Given the potential importance of this process in understanding why the method works, could you provide more clarity on how the negative data is generated and discuss how changing the distribution of negative data affects the results?\n\n- The authors helpfully point out all datasets that were also used as test sets for TabPFN's evaluation since these could potentially be tainted if good practices were not followed on the original TabPFN paper [1].\nI am more concerned however with datasets that were part of the meta-validation set that was used to tune the hyperparameter priors of TabPFN. It seems that one of the datasets used for evaluation of TabEBM (stock) is part of this meta-validation set (Tables 7 and 8 in the appendix of [1]).\nEven though this is only one of 150 datasets that comprise this validation set and it is not clear in the original paper the extent of this finetuning, I would still consider it good practice to avoid using this dataset for evaluating downstream methods for fear of data leakage. I also would have liked the paper to prioritize evaluating on more datasets that weren't used at all in [1]. I understand if [1] might have somewhat exhausted the pool of small datasets in OpenML but evaluating on larger datasets by first subsampling them would be an option. This would also allow for the use of real data as an ideal baseline to measure TabEBM's improvement against.\n\n- For TabEBM and the other methods that learn class conditional densities (CTGAN, TabDDPM, ARF, GOGGLE, TabPFGen) what distribution of classes (i.e., $p(y)$) was used for the synthetic data? This is not specified in the paper so I am assuming it was an empirical estimate of the p(y) from the training data otherwise this would be somewhat unfair when comparing to methods that learn a joint distribution. Furthermore it would be potentially problematic when evaluating a balanced accuracy in a test set if the p(y) of generated data is not the same across methods (for conditional methods).\n\n- How are statistical fidelity results computed? The metrics reported seem to be univariate ones so how are they being used to compare multivariate distributions? Are only marginal distributions being compared? Is it an average over univariate metrics computed for each marginal separately? How is the KS test used on categorical variables? This section of the experiments is sorely lacking in details and the appendices seem to provide no further information. If it is indeed the case that only marginals are being compared I find this evaluation lackluster since it is easy to achieve similar marginal distributions without learning the relationships between different input variables which is the main difficulty in learning multivariate density models.\n\n\n[1] Noah Hollmann, Samuel Müller, Katharina Eggensperger, Frank Hutter. TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second, 2022 (https://arxiv.org/abs/2207.01848)", "limitations": "The authors aknowledge that due to the reliance of the method on a PFN it is currently constrained for use in small datasets.", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The paper is well-structured and clearly written, effectively communicating the key ideas and concepts.\n- The authors introduce a novel approach by leveraging a Prior-Data Fitted Network (PFN) to obtain energy-based models (EBMs), which, to the best of my knowledge, has not been previously explored.\n- The experimental results section is thorough and comprehensive. They compare their approach to a wide range of relevant and competitive methods for synthetic data generation.\n- The appendices are well-organized and provide valuable supplementary information. The paper strikes a good balance with the most relevant information presented in main text and additional details provided in the appendix.", "weaknesses": "- Interpreting classifier logits as energy functions may not necessarily yield good density models. Given a classifier with logits $f(x)[y]$, one can add an arbitrary function $g(x)$ that is constant over $y$, $f(x)[y] \\rightarrow f(x)[y] + g(x)$, without affecting the conditional probabilities $p(y\\vert x)$ due to the invariance of the softmax function to the addition of a constant. However, this changes the energy function for the density model to $E(x) \\rightarrow E(x) - g(x)$. Consequently, there exists a functional degree of freedom that can arbitrarily alter the energy function without impacting the discriminative loss optimized by a classifier. As a result, a classifier trained solely to distinguish between positive and negative samples is not inherently encouraged to learn a useful energy function for the density over $x$.\nMy interpretation of the results of [1], from which the authors seem to draw inspiration is that reinterpreting the logits of a classification model as an energy based model by itself accomplishes nothing if the training process of the original classifier is not changed to encourage a good density model to be learned and encoded into the free degree of freedom. [1] achieves this by optimizing the joint likelihood, $E_{x,y} p_\\theta(y,x)$, instead of the conditional likelihood, $E_{x,y} p_\\theta(y\\vert x)$, used in training classifiers. This significantly complicates training by requiring sampling from the EBM during training. Therefore, it is unclear why the authors assume that the pre-trained PFN has learned useful energy functions for density modeling when it is derived from a simple classifier and this is not discussed in the paper.\n\n- Another weakness of the paper is in the experimental setup where only default hyperparameters are used for all competing methods. For many of these methods, tuning hyperparameters can substantially improve their results and the default hyperparameters may not be optimal.\nPersonally, I would find the presented results more convincing if the paper compared with fewer competing methods but made a better effort of getting good results out of those as it is impossible to know how much the authors tuned the degrees of freedom available during experimentation with their own proposed method.\n\n[1] Will Grathwohl, Kuan-Chieh Wang, Jörn-Henrik Jacobsen, David Duvenaud, Mohammad Norouzi, Kevin Swersky. Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One, 2022 (https://arxiv.org/abs/1912.03263)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the detailed review and constructive feedback! We address **all** your questions and comments below, and provide a **rebuttal PDF** in the general rebuttal. Due to space limits, we summarise the new results. We will update our manuscript with additional clarifications and results.\n\n## >Q3a: Clarify the generation of the negative samples\nThe surrogate classification task is to determine if a sample belongs to class $c$ by comparing $\\mathcal{X}_c$ against a set of \"negative samples\" $\\mathcal{X}_c^{\\text{neg}}$. We label the true samples $\\mathcal{X}_c$ as 1 and the negative samples $\\mathcal{X}_c^{\\text{neg}}$ as 0, and train TabPFN on this datasets, resulting in a class-specific binary classifier used to define the $E_c(x)$ (using Equation 3)\n\nWe generate the negative samples at the corners of a hypercube in $R^D$. For each dimension $d$, the coordinates of a negative sample are either $\\alpha\\sigma_d$ or $-\\alpha\\sigma_d$, where $\\alpha$ is a fixed constant and $\\sigma_d$ is the standard deviation of dimension $d$. For example, in $R^3$, a negative sample might have coordinates $[\\alpha\\sigma_1, \\alpha\\sigma_2, -\\alpha\\sigma_3]$. In the paper we use four negative samples with $\\alpha = 5$, placing them far from the real data.\n\n## >Q3b: How does the distribution of negative data affect the results?\nWe found it essential to use negative samples far from the real data, to allow the binary classifier to easily differentiate between $\\mathcal{X}_c$ and $\\mathcal{X}_c^{\\text{neg}}$.\n\nFigure `F1` from the PDF shows a **new experiment** varying the distribution of the negative samples. TabEBM infers an accurate energy surface with distant negative samples, and the energy surface becomes inaccurate when negative samples resemble real samples. This occurs because TabPFN is uncertain, affecting its logits magnitude and making them unsuitable for density estimation (we further investigate the logits in our next answer to Q1/W1).\n\nTabEBM is robust to the distribution of negative samples if they are easily distinguishable from real data. We ran **two new experiments**, keeping the negative samples at the corners of a hypercube and varying their distance and number. When varying the per-dimension distance of those samples $\\alpha \\in [0.1, 5]$, TabEBM provides consistent improvements between 2.85-3.18%. Additionally, our results in Table `R2` (in our answer to Q1 from reviewer Cc3y) demonstrate that TabEBM performs similarly regardless of the number of negative samples in the surrogate binary tasks.\n\n## >Q1/W1: Why can TabPFN's logits be useful for energy estimation?\nIndeed, we agree with your observation! As the TabPFN classifier is trained on different class-specific surrogate tasks, it learns different logits for each task. We found it essential to place the negative samples far from the real samples, because TabPFN's confidence depends on the distance to the training data [1], as it was pre-trained to approximate Bayesian inference.\n\nWe present **new experiments** in Figure `F2` from the PDF. The top row shows that as the distance to the real data increases, the logit $f(x)[1]$ for the real data smoothly decreases until the two logits become similar. Thus, the classifier predicts is uncertain in these far-away regions. As maximum logits decrease, TabEBM's inferred density drops significantly (as shown on the bottom row) because $p_c(x) \\propto (\\exp(f(x)[0]) + \\exp(f(x)[1]))$. One could possibly fine-tune TabPFN on the surrogate tasks to further improve the logits for density estimation.\n\n## >Q2: Why fit p(x) rather than p(x|y=1) in the surrogate binary tasks?\nBoth approaches lead to virtually identical results due to the design of our surrogate task. The **new results** in Figure `F2` (bottom row) from the PDF shows that the TabEBM's inferred energy using $p(x)$ (in red) is essentially identical to the energy of $p(x|y=1)$ (in grey), especially near the real data. As the SGLD sampling starts near the original points (line 676), it will visit the neighbourhood of the real samples, where the energy surfaces are virtually identical, leading to similar results.\n\n## >Q4: Evaluating more datasets\nWe run **new experiments** on six leakage-free datasets from UCI, with 1,000-9105 samples of 7-42 features. Table `R2` (in our response to Q2 for `tdoQ`) shows that TabEBM consistently outperforms the baseline and all other benchmark methods.\n\n## >Q5: What's the class distribution of the synthetic data?\nThe synthetic data has the same class distribution as the real training data.\n\n## >Q6: Is statistical fidelity computed over the univariate marginals?\nYes, these metrics are univariate, and we computed them using the open-source library Synthcity. We acknowledge the reviewer's point about the imperfection of univariate metrics, although evaluating generators' ability to capture the joint feature relationships remains underexplored ``[2]``.\n\n## >W2: How does tuning the generators/predictors affect the ranking?\nWe run **new experiments** tuning three generators on three datasets using the average validation accuracy of six downstream classifiers. The ranges are: SMOTE ($k \\in \\{3, 5, 10\\}$), TVAE ($\\text{lr} \\in \\{5e-4, 1e-3, 5e-3\\}$) and CTGAN ($\\text{lr} \\in \\{1e-3, 5e-3, 1e-2\\}$). TabEBM remains the most competitive data augmentation method, improving accuracy by +2.25, followed by SMOTE (+1.81) and CTGAN (-5.71). We can provide the full results in the discussion.\n\nWe also tuned the downstream predictors, and the **new results** in Table `R7` from the PDF show that TabEBM remains the best-performing method, providing the largest improvements for data augmentation, even after tuning the predictors.\n\nThank you again for your constructive review! We would appreciate it if you would consider raising your score in light of our response.\n\nReferences:\n- `[1]` McCarter, *What exactly has TabPFN learned to do?*, ICLR Blogposts, 2024\n- `[2]` Tu, Ruibo, et al., 2024, (https://arxiv.org/abs/2406.08311)", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:
We thank the reviewers for the feedback!

## **(1) Summary of positive things**

- **Novel method**
    - `Cc3y`: *“a new method of tabular data augmentation”; “the unique feature is that it creates distinct generative models for each class”*
    - `iojh`: *“Novel approach using class-specific EBMs for tabular data generation”*
    - `XdB4`: *“a novel approach that utilizes separate energy-based models (EBMs) to generate synthetic data for each class”*
- **Comprehensive evaluation showing TabEBM's effectiveness**
    - `tdoQ`: *“thorough experiments demonstrating effectiveness”*
    - `Cc3y`: *“extensive and thorough evaluations”; ”TabEBM sets the new state of the art”*
    - `iojh`: *”Comprehensive evaluation across multiple datasets, metrics, and downstream tasks”; “TabEBM improves downstream performance … generates high-fidelity synthetic data”*
    - `XdB4`: *“The experimental results section is thorough and comprehensive”*
- **Clear presentation**
    - `tdoQ`: *“well-structured and clear”*
    - `Cc3y`: *“The manuscript is well organized”; “The text is clear”; “The quality of the figures is high”*
    - `XdB4`: *“The paper is well-structured and clearly written, effectively communicating the key ideas and concepts.”*
- **Impactful method**
    - `Cc3y`: *“The authors address a very common problem for the broad scientific community”; “this work can have an extremely broad impact in the future”*
- **Reproducibility**
    - `iojh`: *“Open-source implementation provided”*

## **(2) Summary of our responses and new experiments**

We replied to **all** questions and concerns raised by the reviewers:

*Table R0*. Number of our responses to the reviewers’ comments (`#Raised`/`#Replied`).

| Reviewer | # Questions | # Weaknesses | # Limitations | # New experiments |
| --- | --- | --- | --- | --- |
| `tdoQ` | 2/2 | 4/4 | N/A | 1 |
| `Cc3y` | 5/5 | N/A | N/A | 1 |
| `iojh` | 6/6 | 2/2 | 3/3 | 3 |
| `XdB4` | 6/6 | 2/2 | N/A | 5 |

We provide **10 new experiments** and attach a **rebuttal PDF**. The new results are *consistent* with the main text and further support TabEBM’s effectiveness. We will add them to the revised manuscript. Below, we detail the new experiments for each reviewer.

1. `[tdoQ, XdB4]` Evaluation on six new, leakage-free datasets with mixed feature types.
2. `[Cc3y]` Ablation studies on the surrogate binary classification task w.r.t. the imbalance between the negative samples and the real samples.
3. `[iojh]` Evaluation on highly imbalanced datasets to show TabEBM’s robustness.
4. `[iojh]` Ablation studies on TabEBM’s sensitivity to the hyperparameters of the SGLD sampling process.
5. `[iojh]` Evaluation on larger datasets to show TabEBM’s scalability.
6. `[XdB4]` Ablation studies on the distance of the negative samples and the real samples.
7. `[XdB4]` Evaluating the impact of the distribution of the negative samples.
8. `[XdB4]` Investigation into TabPFN's logit values on the surrogate binary tasks.
9. `[XdB4]` Ablation studies on tuning the hyper-parameters of generative benchmarks.
10. `[XdB4]` Ablation studies on tuning the downstream predictors.

Meta-review: The authors propose a generative method for tabular data augmentation, utilizing a distinct generative process for each class in a classification setting.

- **Reviews**: The paper received mostly positive scores, though some were near and one below the threshold. The weaknesses noted were in the areas of novelty, clarity, and missing technical details.
- **Rebuttal**: The authors made significant efforts to address the reviewers' concerns, particularly by providing additional experiments. As a result, two reviewers raised their scores. It appears that the authors successfully addressed most of the points that were raised.
- **Post-decision Revision**: As noted by one reviewer, 
    + the new dataset `collins` seems to have been used to tune TabPFN and hence is not meaningful to derive conclusions from;
    + the statistical fidelity metrics should be better explained, as it is 1) not clear how they are aggregated, 2) the KS metric only considers numerical features, and 3) the KL is potentially based only on categorical features.
Decision: Accept (poster)