DECAF:  Generating Fair Synthetic Data Using Causally-Aware Generative Networks
Authors: Boris van Breugel
Trent Kyono
Jeroen Berrevoets
Mihaela van der Schaar
Venue: NeurIPS 2021 Poster (2021)
Keywords: synthetic data
generative models
fairness

Abstract: Machine learning models have been criticized for reflecting unfair biases in the training data.  Instead of solving for this by introducing fair learning algorithms directly, we focus on generating fair synthetic data, such that any downstream learner is fair. Generating fair synthetic data from unfair data - while remaining truthful to the underlying data-generating process (DGP) - is non-trivial. In this paper, we introduce DECAF: a GAN-based fair synthetic data generator for tabular data.  With DECAF we embed the DGP explicitly as a structural causal model in the input layers of the generator, allowing each variable to be reconstructed conditioned on its causal parents.  This procedure enables inference time debiasing, where biased edges can be strategically removed for satisfying user-defined fairness requirements. The DECAF framework is versatile and compatible with several popular definitions of fairness. In our experiments, we show that DECAF successfully removes undesired bias and - in contrast to existing methods - is capable of generating high-quality synthetic data. Furthermore, we provide theoretical guarantees on the generator's convergence and the fairness of downstream models.

DECAF: Generating Fair Synthetic Data Using Causally-Awars Generative Networks
Boris van Breugel* University of Cambridge
Trent Kyono"
Jeroen Berrevoets University of Cambridge jb23840cam ac.
University of California, Los Angeles tmkyonoQucla.eer edu
bv2920cam. ac
Mihaela van der Schaar
University of Cambridge
University of California, Los Angeles The Alan Turing Institute mv4720cam ac. uk
Abstract
Machine learning models have been criticized for reflecting unfair biases the training data. Instead of solving for this by introducing fair learning algorithms directly, we focus on generating fair synthetic data, such that any downstream learner is fair. Generating fair synthetic data from unfair data- while remaining truthful to the underlying data- teatta-gneratingg process (DGP) -is non-trivial. In this paper, introduce DECAF: GGAN-bsee fair synthetic data generator for tabular data. With DECAF we embed the DGP explicitly as a structural causal model in the input layers of the generator, allowing each variable be reconstructed conditioned on its causal parents. This procedure enables inference-time debiasing, where biased edges can strategically removed for satisfying user-defined fairness requirements. The DECAF framework is versatile and compatible with several popular definitions of fairness. In our experiments, we show that DECAF success- fully removes undesired bias and- in contrast to existing methods -is capable of generating high-quality synthetic data. Furthermore, we provide theoretical guarantees on the generator's 's convergence and the faimess of downstream models.
Introduction
Generative models are optimized to approximate the original data distribution as closely possible. Most research focuses on three objectives [1]: fidelity, diversity, and privacy. The first and second are concerned with how closely synthetic samples resemble real data and how much of the real data's distribution is covered by the new distribution, respectively. The third objective aims to avoid simply reproducing samples from the original data, which is important if the data contains privacy-sensiteee information [2. 3J. We explore much-less studied concept: synthetic data fairness.
Motivation. Deployed machine learning models have been shown to reflect the bias of the data which they are trained [4, 5, 6, 7, 8). This has not only unfairly damaged the discriminated individuals but also society's 's trust in machine learning as whole. A large body of work has explored ways of detecting bias and creating fair predictors [9. 10, 11, 12, 13, 14, 15], while other authors propose debiasing the data itself [9. 10, 11, 16). This work's 's aim is related to the work of [17]: generate fair synthetic data based on unfair data. Being able to generate fair data is important because end-users creating models based publicly available data might be unaware they are inadvertently including
Equual contribution
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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Table Overview of related work for synthetic data. We organize related work according to our key areas of interest: (1) Allows post-hoc distribution changes, (2) provides faimess, (3) supports causal notion of fairness, (4) allows tifrrecc--imme fairness, (5) requires minimal assumptions. We
highlight the key contribution, and identify non-neural approaches with "T".
Model
Reference
(1) (2) (3) (4) (5) Goal
Standard synthetic data generation
VAE
[19]
X
Realistic synth. data. Realistic synth. data.
GANs
[2, 3, 20, 21]
x
x
x
Methods that detect and/or remove bias
PSE-DD/DR
[11]
/
X
Discover/Remove bias.
OPPDP
[16]
X
/
x
X
X
Remove bias.
DIT
[10]
X
/
X
X
X
Discover/Remove bias.
LFR
[22]
X
Learn fair representation. Realistic and fair synth. data. Realistic and fair synth. data.
FairGAN
[17]
V
X
X
CFGAN
[23]
/
V
DECAF
(ours)
Realistic and fair synth. data.
bias or insufficiently knowledgeable to remove it from their model. Furthermore, by debiasing the data prior to public release, one can guarantee any downstream model satisfies desired fairness requirements by assigning the responsibility of debiasing to the data generating entities.
Goal. From biased dataset X' we are interested learning a model G, that is able to generate an equivalent synthetic unbiased dataset X' with minimal loss of data utility. Furthermore, downstream model trained on the synthetic data needs to make not only unbiased predictions on the synthetic data, but also on real-life datasets (as formalized in Section 4.2).
Solution. We approach fairness from causal standpoint because provides an intuitive perspective on different definitions of fairness and discrimination [11, 13, 14, 15, 18]. We introduce DEbiasing CAusal Fairness (DECAF), generative adversarial network (GAN) that leverages causal structure for synthesizing data. Specifically, DECAF is comprised of d generators (one for each variable) that learn the causal conditionals observed in the data. At inference-time, variables are synthesized topologically starting from the root nodes in the causal graph then synthesized sequentially, terminating at the leave nodes. Because of this, DECAF can remove bias inference-time through targeted (biased) edge removal. As result, various datasets can be created for desired (or evolving) definitions of fairness.
Contributions. We propose framework of using causal knowledge for fair synthetic data generation. We make three main contributions: i) DECAF, a causal GAN- basebased model for generating synthetic data, ii) flexible causal approach for modifying this model such that can generate fair data, and iii) guarantees that downstream models trained on the synthetic data will also give fair predictions in other settings. Experimentally, we show how DECAF is compatible with several faimess//iscriminatio definitions used in literature while still maintaining high downstream utility of generated data.
2 Related Works
Here focus the related work concerned with data generation, in contrast to fairness definitions for which we provide a detailed overview in Section 4 and Appendix C. As an overview of how data generation methods relate one another, we refer Table which presents all relevant related methods.
Non- parametricc generative modeling. The standard models for synthetic data generation either based on VAEs [19] or GANs [2, 3, 20, 21J. While these models are well known for their highly realistic synthetic data, they are unable to alter the synthetic data distribution to encourage faimess (except for [17, 23], discussed below). Furthermore, these methods have no causal notion, which prohibits targeted interventions for synthesizing fair data (Section 4). We explicitly leave out CAusalGAN [24] and CausalVAE [25], which appear similar by incorporating causality-derive ideas but are different in both method and aim (i.e., image generation).
Fair data generation. In the bottom section of Table we present methods that, in some way, alter the training data of classifiers to adhere to notion of fairness [10, 11, 16, 17, 22, 23]. While

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these methods have proven successful, they lack some important features. For example, none of the related methods allow for post-hoe changes of the synthetic data distribution. This is an important feature, as each situation requires a different perspective on fairness and thus requires a flexible framework for selecting protected variables. Additionally, only [11, 23] allow a causal perspective on fairness, despite causal notions underlying multiple interpretations of what should be considered fair [13]. Furthermore, only [17, 22, 23] offer a flexible framework, while the others are limited to binary [10, 11] or discrete [16] settings. Xu et al. [23] also use causal architecture for the generator, however their method is not as flexible-e.2 e.g. it does not easily extend to multiple protected attributes. Finally, in contrast to other methods DECAF is directly concerned with fairness of the downstream model-which is dependent on the setting in which the downstream model is employed (Section 4.2). In essence, from Table I we learn that DECAF is the only method that combines all key areas of interest. At last, we would like to mention [26], who aim to generate data that resembles a small unbiased reference dataset, by leveraging large but biased dataset. This is very different to our aim, as we are interested in the downstream model's fairness and explicit notions of fairness.
3 Preliminaries
Let E X' C Rd denote a random variable with distribution Px(X). with protected attributes A E A C X' and target variable Y E y C X, let Y denote prediction of Y. Let the data be given by D= = (x( M where each (*) E D is a realization of X. We assume the data generating process can be represented by directed acyclic graph (DAG)-such that the generation of features can be written as structural equation model (SEM) [27]-and that this DAG is causally sufficient. Let X; denote the zth feature in X with causal parents Pa (a(X;) C (X; : j f i}, the SEM given by:
X (Pa(X)), Z.), Vi
where {2 are independent random noise variables, that is Pa(Z,) = 0, Vi. Note that each f. is a deterministic function that places all randomness of the conditional P(X,) Pa(X.)) in the respective noise variable, Z..
4 Fairness of Synthetic Data
Algorithmic fairness a popular topic (e.g., see [13, 28)), but fair synthetic data has been much less explored. This section highlights how the underlying graphs of the synthetic and downstream data determine whether a model trained on the synthetic data will be fair in practice. We start with the two most popular definitions of fairness, relating to the legal concepts of direct and indirect discrimination. We also explore conditional fairness Appendix C discuss how the ideas in this section transfer other independence-basee definitions [30]. Throughout this section, we separate Y from X by defining X = X\Y, and we will write X + X for ease of notation.
faireess [29], which is generalization of the two. In
4.1 Algorithmic fairness
The first definition is called Fairness Through Unawareness (e.g. [31]).
Definition 1. (Fairness Through Unawareness (FTU): algorithm)). A predictor f X & is fair iff protected attributes are not explicitly used by to predict Y
This definition prohibits disparate treatment [28, 32], and is related to the legal concept of direct discrimination, i.e., two equally qualified people deserve the same job opportunity independent of their race, gender, beliefs, among others.
Though FTU fairness commonly used, it might result indirect discrimination: covariates that influence the prediction might not be identically distributed across different groups a, a', which means an algorithm might have disparate impact on a protected group [10]. The second definition of fairness, demographic parity [32], does not allow this:
Definition 2. (Demographic Parity (DP): algorithm) A predictor Y is fair iff A IL Y, i.e. Va, a': P(Ý A= = a) P( a').
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Evidently, DP puts stringent constraints on the algorithm, whereas FTU might be too lenient. The third definition we include is based on the work of [29], related unresolved discrimination [14]. The idea is that we do not allow indirect discrimination unless it runs through explanatory factors R C X. For example, in Simpson's paradox [33] there seems to be bias between gender and college admissions, but this is only due to women applying to more competitive courses. In this case, one would want to regard fairness conditioned on the choice of study [14]. Let us define this as conditional fairness:
Definition 3. (Conditional Fairness (CF): algorithm) A predictor Y is fair iff A TL YRR, i.e. Vr, a,a' P(Y) = r, = a) P( = r, = d').
CF generalizes FTU and DP Note that conditional fairness is a generalization of FTU and DP, by setting R X (A and R 0, respectively. In Appendix C we elaborate on the connection between these, and more, definitions.
4.2 Synthetic data fairness
Algorithmic definitions can be extended distributional fairness for synthetic data. Let P(X), P'(X) be probability distributions with protected attributes A C X and labels Y C X. Let I(A, Y) be definition of algorithmic faimess (e.g.. FTU). Note, that under CF, I(A,Y) is a function of R as well. We propose (I(A, Y), Pa-firmssss of distribution P'(X):
Definition 4. (Distributional fairness) A probability distribution P' P'(X) is (I(A,Y). P)-fair iff the optimal predictor y = ff((x) Y trained on P' P'(X) satisfies I(A,Y) when evaluated on P(X).
In other words, when we train predictor (IA,Y). -fir distribution P') we can only reach maximum performance if our model is fair. Note the explicit reference to P(X). the distribution on which faimess is evaluated, which does not need to coincide with PX)) This is small but relevant detail. For example, when training a model on data D' ~ P'(X)) it could seem like the model is fair when we evaluate on a hold-out set of the data (e.g., if we simply remove the protected attribute from the data). However, when we use the model for real-world predictions of data D ~ P(X), disparate impact is possibly observed due to distributional shift.
By extension, we define synthetic data as (I(A, P)-fair, iff it is sampled from an (I(A, Y), P)- fair distribution. Defining synthetic data fair w.r.t. optimal predictor is especially useful when we want to publish a dataset and do not trust end-users to consider anything but performance.?
The setting P(X) P'(X) corresponds to data being fair with respect to itself. For synthetic data generation, this setting is uninteresting as any dataset can be made fair by randomly sampling or removing A; if A is random, the prediction should not directly or indirectly depend on it. This ignores, however, that a downstream user might use the trained model on real-world dataset in which other variables B are correlated with A, and thus their model (which is trained to use B for predicting Y) will be biased. Of specific interest the setting where P(X) corresponds to the original data distribution Px (X) that contains unfairness. In this scenario, construct P'(X) by learning Px (X) and removing the unfair characteristics. The data from P" ("() can be published online, and models trained on this data can be deployed fairly in real-life scenarios where data follows (x).). Unless otherwise stated, henceforth, we assume P(X) = PX)..
Choosing P(X).
4.3 Graphical perspective
As reflected in the widely accepted terms direct versus indirect discrimination, it is natural to define distributional fairness from a causal standpoint. Let G' and G respectively denote the graphs underlying P'(X) (the synthetic data distribution which we can control) and P(X) (the evaluation distribution that we cannot control). Let 0g Y denote the Markov boundary of Y in graph G. We focus on the conditional fairness definition because it subsumes the definition of DP and FTU (Section 4.1). Let R C X be the set of explanatory features.
Proposition 1. (CF: graphical condition) for all B E 0g A 11g B R then distribution PX(X) is CF fair w.r.t P(X) given explanatory factors R.
FFinding the optimal predictor is possible we assume the downstream user employs any universal function approximator (c.g.. ML.) and the amount of synthetic data sufficiently large. Where 11g denotes d deseparation in G. Here we detine A 11g B|R to be true for all B R.

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Proof. Without loss of generality, let us assume the label is binary.* The optimal predictor (X) P(Y X) = P(Y ((rr)ag ). Thus, if 0g Y is d-separated from A in 9 given R. prediction Y (X) is independent of A given Rt and CF holds.
Corollary 1. (CF debiasing) Any distribution (x with graph G' can be made CF fair w.r.t f.i...r.. P(X) and explanatory features R by removing from G' edges E = {{B + Y) and (Y - B) : VB dg.Y with B g A
Proof. First note E is the necessary and sufficient set of edges to remove for (vB E ag. Y, A 1 B R) be true, subsequently the result follows from Proposition I.
For FTU (i.e. R= and DP (i.e. R = 0), this corollary simplifies to:
Corollary 2. (FTU debiasing) Any distribution (X( with graph G' can be made FTU fair w.r.l any distribution P(X) by removing, if present, i) the edge between A and Y and i) the edge A - C or + C for all shared children C.
B
Corollary 3. (DP debiasing) Any distribution (X) with graph G' can be made DP fair w.r.t. P(X) by removing, if present, the edge between B and for any B 0g. Y with B Ag A.
Figure 1: Edge re- moval for fairness. FTU: X: DP: XXX; CF when R C: XX; CF
Figure shows how the different fairness definitions lead to different sets of edges to be removed.
when B E R: X
Faithfulness. Usually one assumes distributions are faithful w.r.t. their respective graphs, in which case the if-statement in Proposition 1 become equivalence statements: fairness is only possible when the graphical conditions hold.
Theorem 1. If P(X) and (X( are faithful with respect to their respective graphs G and G'. then Proposition 1 becomes an equivalence statement and Corollaries 2 and describe the necessary and sufficient sets of edges to remove for achieving CF, FTU and DP fairness, respectively.
Proof. Faithfulness implies A P()) B = A lig B|R, e.g. [34). Thus, iB 0g.Y for which A g B) R, then y.. B. Because E Yg and P'(X) is faithful to g', y = (X)
depends on B, and thus Y y A A:: CF does not hold.
Other definitions. Some authors define similar fairness measures terms of directed paths (cf. d-separation) [11, 14, 18], which is milder requirement as it allows correlation via non-causal paths. In Appendix we highlight the graphical conditions for these definitions.
Method: DECAF
The primary design goal of DECAF is to generate fair synthetic data from unfair data. We separate DECAF into two stages. The training stage learns the causal conditionals that observed in the data through a dausally-informer GAN. At the generation (inference) stage, we intervene on the learned conditionals via Corollaries 1-3, in such way that the generator creates fair data. We assume the underlying DGP's graph G is known; otherwise, & needs to be approximated first using any causal discovery method, see Section 6.
5.1 Training
Overview. This stage strives to learn the causal mechanisms ()((P((X)), Z.)). Each structural equation fa (Eq. 1) is modelled by separate generator G; R1Px(X - lR. We achieve this by employing a conditional GAN framework with a causal generator. This process is illustrated in Figure and detailed below.
'Ir Y is continuous the same result holds, though the "optimal" predictor will depend on the statistic of interest, e.g. mode, mean, median the entire distribution f(X, Y) XX).
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Training phase
Inference phase
Y
B
Fair DAG
GA
GB
Discriminator
Xa(X.)
Pa(
Requires causal information
Parents based intervened DAG
Figure 2: Architecture. Training phase- Each component in X is generated sequentially function (where the function is that component's generator G:) of the component's parents. Parental knowledge provided by the DAG governing the data. Inference phase- As the component-wiss generation of the generator network is independent of the DAG governing the data, we can easily replace (or intervene on) the DAG governing parental information. The resulting synthetic data (right) will be governed by the intervened DAG. FTU is achieved by removing: X; DP: XXX; e.g. CF when R = C: xX.
Features are generated sequentially following the topological ordering of the underlying causal DAG: first root nodes are generated, then their children (from generated causal parents), etc. Variable X, is modelled by the associated generator G₁;:
X, G, (Pa(()) Zz) Vi,
where Pa(X;) denotes the generated causal parents of X; (for root nodes the empty set), and each Z; is independently sampled from P(Z) (e.g. standard Gaussian). We denote the full sequential generator by G(Z) = (Z1) ....y Ga(:: Za)]
Subsequently, the synthetic sample x is passed to discriminator D ; Rd R, which is trained to distinguish the generated samples from original samples. A typical minimax objective is employed for creating generated samples that confuse the discriminator most:
max min Ellog D(G(Z)) + log(1 - D(X)). (G.) D
(3)
with X sampled from the original data. We optimize the discriminator and generator iteratively and
add regularization loss to both networks. Network parameters are updated using gradient descent.
If assume Px (X) is compatible with graph G, we can show that the sequential generator has the same theoretical convergence guarantees as standard GANs [20]:
Theorem 2. (Convergence guarantee) Assuming the following three conditions hold:
(i) data generating distribution Px is Markov compatible with a known DAG 9;
(ii) generator G and discriminator have enough capacity; and
(ii)) in every training step the discriminator is trained optimality fixen G, and G is subse- quently updated as to maximize the discriminator loss (Eq. 3);
then generator distribution PG converges to true data distribution Px
Proof. See Appendix B
Condition (i), compatibility with G, is weaker assumption than assuming perfect causal knowledge. For example, suppose the Markov equivalence class of the true underlying DAG has been determined through causal discovery. In that case, any graph G in the equivalence class is compatible with the data and can thus be used for synthetic data generation. However, we note that debiasing can require the correct directionality for some definitions of fairness, Discussion.
The causal GAN we propose, DECAF, simple and extendable to other generative methods, e.g., VAFs. Furthermore, from the post-processing theorem [35] it follows that DECAF can be directly used for generating private synthetic data by replacing the standard discriminator by differentially private discriminator [2, 36].
Remark.

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5.2 Inference-time Debiasing
The training phase yields conditional generators {G,) which can be sequentially applied to generate data with the same output distribution the original data (proof in Appendix B). The causal model allows us to go one step further: when the original data has characteristics that we do not want to propagate the synthetic data (e.g., gender bias), individual generators to remove these characteristics. Given the generator's graph G = (X, F),, fairness is achieved by removing edges such that the faimess criteria are met, see Section 4. Let E E E be the set of edges to remove for satisfying the required fairness definition. For CF. FTU and DP, the sets E are given by Corollaries 1, and 3, respectively.
be modified
Removing an edge constitutes to what we call a "surrogate" do-operation [27] on the conditional distribution. For example, suppose we only want to remove (i - j). For given sample, X, is generated normally (Eq. 2), but X, is generated using the modified:
X xdo(X = -Gy X; = Tzy);
(4)
where X; Tay is the surrogate parent assignment. Value xxx((x)) can be interpreted as the counterfactual value of X,, had X; been equal to žis (see also [15]).
Choosing the value of surrogate variable Haz requires background knowledge of the task and bias hand. For example, surrogate variable ēæj can be sampled independently from a distribution for each synthetic sample (e.g., the marginal P(X.)). be set to fixed value for all samples in the synthetic data (e.g., if X₁: gender, always set Tzj = male when generating feature Xy: job opportunity) or
be chosen as to maximize/minimize some feature (e.g. žig arg max; X xdd((i)==>) We emphasize that we do not set X, Øig in the synthetic sample; X, = f.g is only used for substitution of the removed dependence. We provide more details in Appendix E.
More generally, we create surrogate variables for all edges we remove, (ā. (i + j) E EJ. Each sample is sequentially generated by Eq. 4, with a surrogate variable for each removed incoming edge.
Remark. Multiple datasets can be created based on different definitions fairness and/or different downstream prediction targets. Because debiasing happens at inference-time, this does not require retraining the model.
6 Experiments
In this section, we validate the performance of DECAF for synthesizing bias-free data based on two datasets: i) real data with existing bias and ii) real data with synthetically injected bias. The aim of the former is show that we can remove real, existing bias. The latter experiment provides a ground-truth unbiased target distribution, which means we can evaluate the quality of the synthetic dataset with respect to this ground truth. For example, when historically biased data is first debiased, model trained on the synthetic data will likely create better predictions in contemporary, unbiased/less-biasee settings than benchmarks that do not debias first
In both experiments, the ground-trute truth DAG is unknown. We use causal discovery to uncover the underlying DAG and show empirically that the performance is still good.
Benchmarks. We compare DECAF against the following benchmark generative methods: GAN, a Wasserstein GAN with gradient penalty (WGAN-GP) [21] and FairGAN [17]. FairGAN is the only benchmark designed to generate synthetic fair data, whereas GAN and WGAN-GP only aim to match the original data's 's distribution, regardless of inherent underlying bias. For these benchmarks, fair data can be generated by naively removing the protected variable we refer to these methods with the PR (protected removal) suffix and provide more experimental results and insight into PR in Appendix A. We benchmark DECAF debiasing in four ways: i) with no inference time debiasing
Just like in Corollaries I and 3, assume the downstream evaluation distribution is the same as the biased training data distribution: a predictor trained on the synthetic debiased data, is required to give fair predictions real-life settings with distribution (X).
'hhe works of [11, 16] are not applicable here, these methods constrained to discrete data.
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Table 2: Bias removal experiment on the Adult dataset [40]. The full table with protected attribute removal can be found in Appendix A.
Data Quality
Fairness
Method
Precisiont
Recall
AUROCT
FTUL
DP1
Original data D
0.920 = 0.006
0 +: 0.008
0,807 = 0.004
0.116 + 0.028
0.180 + 0.010
GAN
0.607 1 0.080
0.439 1 0.037
0.567 : 0.132
0.023 1: 0.010
0.089 1 0.008
WGAN-GP
0.683 + 0.015
0.914 + 0.005
0.798 = 0.009
0.120
0.189 0.024
FairGAN
0.681 1 0.023
0.814 + 0.079
0.766 = 0.029
0.009 0.002
0.097 1 0.018
DECAF-ND
0.780 0.023
0.920 0.045
0.781 = 0.007
0.152 0.013
0.198 1 0.013
DECAF-FTU
0.763 + 0.033
0.925 0.040
0.765 0.010
0.004:1..00
0.054 0.005
DECAF-CF
0.743 0.022
0.875 0.038
0.769 0.004
0.003 + 0.006
0.039 0.011
DECAF-DP
0.781 0.018
0.881 4 0.050
0.672 = 0.014
0.001 1 0.002
0.001 0.001
(DECAF-ND), ii) under FTU (DECAF-FTU), iii) under CF (DECAF-CF) and iv) under DP fairness (DECAF-DP). We provide DECAF implementation details Appendix D.1.
Evaluation criteria. We evaluate DECAF using the following metrics:
Data quality is assessed using metrics of precision and recall [37, 38, 391. Additionally, evaluate all methods in terms of AUROC of predicting the target variable using a downstream classifier (MLP in these experiments) trained synthetic data.
FTU is measured by calculating the difference between the predictions of a downstream
classifier for setting A to and O, respectively, such that [ while keeping all other features the same. This difference measures the direct influence of A on the prediction.
PA=1 ())),,
DP is measured in terms of the Total Variation [15]: the difference between the predictions of a downstream classifier in terms of positive to negative ratio between the different classes of protected variable A, i.e., JP()) A = 0) - P(YJA 1)[-
6.1 Debiasing Census Data
In this experiment, we are given a biased dataset D ~ P(X) and wish to create a synthetic (and debiased) dataset DD, with which downstream classifier can be trained and subsequently be rolled out in setting with distribution P(X). We experiment on the Adult dataset [40], with known bias between gender and income [10, 11]. The Adult dataset contains over 65,000 samples and has 11 attributes, such age, education, gender, income, among others. Following [1 I], we treat gender as the protected variable and use income as the binary target variable representing whether a person carns over $50K not. For DAG G, we use the graph discovered and presented by Zhang et al. [11]. In Appendix D.2, we specify edge removals for DECAF-DP, DECAF-CF, and DECAF-FTU.
Synthetic data is generated using each benchmark method, after which separate MIP is trained on each dataset for computing the metrics; see Appendix D.2 for details. We repeat this experiment 10 times for each benchmark method and report the average in Table 2. As shown, DECAF-NI (no debiasing) performs amongst the best methods in terms of data utility. Because the data utility in this experiment is measured with respect to the original (biased) dataset, we see that the methods DECAF-FTU, DECAF-CE, and DECAF-DP score lower than DECAF-ND because these methods distort the distribution with DECAF-DP distorting the label's conditional distribution most and thus scoring worst in terms of AUROC. Note also that a downstream user who is only focused on performance would choose the synthetic data from WGAN-GP or DECAF-ND, which also the most biased methods. Thus, we see that there is a trade-off between fairness and data utility when the evaluation distribution P(X) is the original biased data.
6.2 Fair Credit Approval
In this experiment, direct bias, which was not previously present, is synthetically injected into a dataset DD resulting in a biased dataset D. We show how DECAF can remove the injected bias, resulting in dataset D' that be used to train downstream classifier. This is relevant scenario if the training data D does not follow real-world distribution P(X), but instead biased distribution P(X) (due to, e.g., historical bias). In this case, we want downstream models trained on synthetic data D' to perform well on the real-world data D instead of D. We show that DECAF successful at removing the bias and how this results in higher data utility than benchmarks methods trained on D.
PPyTorc Lightning source code at ht https: // //gi /gtbtttttubu... http///anddeeeccaraall/aaaeeeeee
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0.90
FAGGH
3.2
DECKSIT
64-
DOGATTT
0.85
NURDC
0.40
62-
Restesurt DOCE
62-
0.0
6lag
Blas
(a) Precisiont
(b) Recallt
(c) AUROCT
(d) FTU
(e) DPL
Figure 3: Plot of precision (a), recall (b), AUROC (c), FTU (d), and DP (e) over bias strength
3. FairGAN performs similarly in terms DP and FTU, but DECAF-FTU and DECAF-DP have significantly better data quality well as down stream prediction capability (AUROC).
We use the Credit Approval dataset from [40], with graph G as discovered by the causal discovery algorithm FGES [41] using Tetrad [42] (details in Appendix D.3). We inject direct bias by de- creasing the probability that sample will have their credit approved based on the chosen A. The credit_approvat for this population was synthetically denied (set 0) with some bias probability 3, adding a directed edge between label and protected attribute.
In Figure 3, we show the results of running our experiment 10 times over various bias probabilities B. We benchmark against FairGAN, as it is the only benchmark designed for synthetic debiased data. Note that in this case, the causal DAG has only one indirect biased edge between the protected variable (see Appendix D), and thus DECAF-DP and DECAF-CF remove the same edges and are the same for this experiment. The plots show that DECAF-FTU and DECAF-DP have similar performance to FairGAN terms of debiasing; however, all of the DECAF_* methods have significantly better data quality metries: precision, recall, and AUROC. DECAF-DP is one of the best performers across all of the evaluation metrics and has better DP performance under higher bias. As expected, DECAF-ND (no debiasing) has the same data quality performance in terms of precision and recall as DECAF-FTU and DECAF-DP and has diminishing performance in terms of downstream AUROC, FTU, and DP as bias strength increases. See Appendix D for other benchmarks, and the same experiment under hidden confounding in Appendix G.
7 Discussion
We have proposed DECAF, a causally-aware GAN that generates fair synthetic data. DECAF's sequential generation provides a natural way of removing these edges, with the advantage that the conditional generation of other features is left unaltered. We demonstrated on real datasets that the DECAF framework is both versatile and compatible with several popular definitions of fairness. Lastly, provided theoretical guarantees on the generator's 's convergence and fairness of downstream models. We next discuss limitations as well as applications and opportunities for future work.
Definitions. DECAF achieves fairness by removing edges between features, as we have shown for the popular FTU and DP definitions. Other independence- based [30] fairness definitions can be achieved by DECAF too, as we show in Appendix C. Just like related debiasing works [10, 11, 16, 17], DECAF not compatible with fairness definitions based on separation or sufficiency [30], as these definitions depend on the downstream model more explicitly (e.g. Equality of Opportunity [12]). More on this in Appendix C.
Incorrect DAG specification. Our method relies on the provision of causal structure in the form of DAG for i) deciding the sequential order of feature generation and ii) deciding which edges to remove to achieve fairness. This graph need not be known a priori and can be discovered instead. If discovered, the DAG needs not equal the true DAG for many definitions of fairness, including FTU and DP, but only some (in)dependence statements are required to be correct (see Proposition 1). This is shown in the Experiments, where the DAG was discovered with the PC algorithm [47] and TETRAD [42]. Furthermore, in Appendix B we prove that the causal generator converges to the right distribution for any graph that is Markov compatible with the data. We reiterate, however, that knowing (part of) the true graph is still helpful because i) it often leads to simpler functions {fr ) to approximate," and ii) some causal faimess definitions do require correct directionality see Appendix
'We let A equal (anonymized) ethnicity [43, 44, 45, 46J, with randomly chosen A = as the disadvan- taged population.
"Specifically, this is the case if modeling the causal direction is simpler than modeling the anti-causal direction. For many classes of models this is true when algorithmic independence holds, see [34].

---

C. In Appendix F, we include an ablation study on how errors in the DAG specification affect data quality and downstream fairness.
Causal sufficiency. We have focused on just one type of graph: causally-suffcciet directed graphs. Extending this undirected or mixed graphs is possible as long as the generation order reflects valid factorization of the observed distribution. This includes settings with hidden confounders. We note that for some definitions of bias, e.g., counterfactual bias, directionality essential and hidden confounders would need to be corrected for (which is not generally possible).
Time-series. We have focused on the tabular domain. The method can be extended other domains with causal interaction between features, e.g., time-series. Application to image data is non-trivial, partly because, in this instance, the protected attribute (e.g.. skin color) does not correspond to single observed feature. DECAF might be extended to this setring in the future by first constructing a graph in disentangled latent space (e.g., [24, 25)).
Social implications. Fairness is task and context-dependent, requiring careful public debate. With that being said, DECAF empowers data issuers take responsibility for downstream model fairness. We hope that this progresses the ubiquity fairness machine learning.
Acknowledgements
We would like to thank the reviewers for their time and valuable feedback. This research was funded by the Office of Naval Research and the WD Armstrong Trust.
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13


Reviews:
[{"review_id": "tkO6bortmUF", "reviewer": "Reviewer_xuZf", "summary": "This work tackles the problem of fairness from a pre-processing perspective by handling the data first using some form of generative transformation. In particular, they use a GAN as this generation and embed a causal structure within the layers. There are then theoretical guarantees presented on the convergence and guarantees of fairness when using the processed data on other tasks.", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "The goal is the submission is to make work towards handling bias in machine learning systems but in particular take a pre-processing approach to this. Overall, such an approach has modularity since any high-performing or even biased algorithm can then use this method to produce fair ML systems, attesting to the significance of this approach.\n\nThe major strength of this submission is precisely this method due to its modularity, which as illustrated seems to be a practical method for practitioners. The weakness I see in this work are the theoretical guarantees, which seem to be quite implicit and lacking - for example, can the authors provide some kind of convergence rates as opposed to just guarantees? On first reading of 'convergence guarantees of the generator', I expected some form of distributional convergence or functional convergence (since they mention the generator will converge) so it would be better if the authors can be more candid about this contribution in the abstract. However, I do not think this is such a major concern. \n\nI am not an expert in this area however the proposal of a GAN-based method that embeds causal structure seems to be quite original and the relevant work seems to be discussed. The paper is well-written with the relevant notation being self-contained and motivation spelled out clearly. I briefly checked the proofs and think the quality of correctness makes sense.\n\nOverall, I rate this paper above the threshold due to the modularity of the approach however since it is not my expertise I cannot comment entirely on the novelty. I think this work is highly relevant to the NeurIPS community and certain can benefit practitioners. One question I had for the authors to better understand this work is: How would this method perform if you trained a GAN on the pre-processed data to create larger datasets?", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes they have.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "8"}, "extra_text": {}}, {"review_id": "kbLIUPsFK6f", "reviewer": "Reviewer_FVou", "summary": "This paper proposes a GAN based causal aware generative model to generate fair data for downstream models. They provide theoretical motivation and practical solutions with different causal criteria. ", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "Pros:\n* This paper considers using a causal aware generative model to generate fair datasets, which I believe is the right approach to handle this problem. \n* The paper is presented clearly\n* The paper provides a theory to motivate the proposed solution \n* The paper has a meaningful discussion regarding how the method can be used in practice (tool for discovery and markove compatible) \n\nCons:\n* Concerns regarding stability of the method (2 below)\n* Concerns about biased data leads to wrong DAG, which cannot generate fair data (point 5 below)\n\n5 is my main concern below comparing to others, and I am looking forward to your reply and happy to change the score if 5 can be addressed. \n\nDetails: \n\n1. You seem need to assume to know the underlying downstream task. If the task selects a different variable as a target, the fairness guarantee won't be there anymore, right? Do you have any thoughts on generating fair datasets generation? \n2. I have concerns about the scalability of the method. If it is tabular data with many variables and with many edges, how would you implement it? ALso, do you need to write a new piece of code given any new causal graph or do you automate it in some way? If so, how?\n3. Causal graph is known is a strong assumption. But it is fine as you discussed discovery methods. In this case, do you have results for your method with respect to error from causal discovery?\n4. line 208. You mentioned Markov compatible and in experiments, you used Tetrad. I assume that the output from the Tetrad with score-based method will be a CPDAG. How did you use CPDAG to design the generator? Did you just take one sample from the Markov equivalent class. How robust is your method to different DAG in the Markov equivalent class? Does these make a difference in experiments?\n5. I believe that causal sufficiency is an assumption here.  However, bias in the dataset itself may be due to selection bias. And existing causal discovery methods have problems to hand selection bias. Thus, the root of the bias cannot to resolved. (the root cause of unfair also it the root cause of the failure of causal discovery methods. ) For example, in 20s the survey about IQ, gender etc where there is fewer females in university where the survey is taken and leads to wrong conclusions. Such selection bias makes causal discovery fail and also makes other ML methods unfair. [Check causal discovery for MNAR papers]\n6. From the generative modeling point of view, the model seems just the GAN version of the CAMA model Zhang C, Zhang K, Li Y. A Causal View on Robustness of Neural Networks. Advances in Neural Information Processing Systems. 2020;33. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "This paper is on the topic of responsible AI and if successful. It brings a more positive impact to machine learning applications. There is no explicit discussion regarding the potential negative societal impact. But I do encourage the authors to discuss more if people rely on their method (which may contain error from causal graph or model training), how to communicate to people about the results, and fairness guarantees. Also, consider how to communicate the assumptions to users to make sure that the methods are used correctly. ", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "jL_JaGbMEWT", "reviewer": "Reviewer_SA2b", "summary": "This work proposes a novel task of generating fair synthetic data by a GAN-based model. The generation process follows the order on a causal DAG and fairness is achieved by debiasing during the inference phase. Experiment results are carried out on Adult and Credit Approval datasets to show the effectiveness of generating fair synthetic data. \n", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "Originality: \n- Generating fair synthetic data for machine learning is an interesting task. This paper designed a GAN-based framework which can achieve fair data generation by simply intervening the inference phase. The idea is novel and interesting. \n\nQuality:\n- Some discussion on efficiency: Although the idea of generating synthetic data following a topological order is an interesting idea, it also raises a concern about the efficiency of the algorithm. The algorithm needs to run the generator d times, where d is the number of columns in the table. If there are only a few protected columns, it’s possible to simplify the DAG by merging irrelevant columns. However, if the number of protected columns are also large, then there’s no easy fix to the efficiency. \n- Comparing with more baseline methods: The method is only compared with GAN-based baselines. Since statistical methods are also capable of generating synthetic data, such baselines should also be included, for example PrivBayes [1]. Also, there are GANs (TableGAN [2], CTGAN [3]) and VAEs (TVAE [3]) designed specifically for synthetic table generation. \n- The experiment is carried out on 2 small dataset, each with less than 20 columns. It’s unclear how the model would perform on a dataset with more columns.  \n\nClarity\n- This paper clearly defines different fairness in synthetic data. The high-level idea is also understandable.\n- However, I would ask the authors to precisely describe the GAN model using either pseudo code or equations in the main paper, rather than burying all details deeply in the supplementary material and even in the source code. For example, the sharing weights in D.1 is important and quite hard to understand. It’s also unclear how the paper handles categorical (discrete) columns in tabular data. \n- I also recommend the authors also provide stats for fair credit dataset. \n\nSignificance: \n- This paper clearly lays out different definitions of fair synthetic data, and the proposed method is novel and interesting. These ideas are inspiring for future research. \n\n[1] PrivBayes: Private Data Release via Bayesian Networks\n[2] Data Synthesis based on Generative Adversarial Networks\n[3] Modeling Tabular data using Conditional GAN\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "I don’t think this work can lead to any negative social impact. \n", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "DACyQUcHxuC", "reviewer": "Reviewer_tL8r", "summary": "This paper proposes DECAF, a fair data generation method using causal DAG structures and GANs. The DAG is used to remove any causal dependencies that may have a negative effect on the fairness and is general enough to model various fairness measures: FTU, DP, and CF. Then synthetic data is generated according to the DAG, but made realistic using a discriminator that distinguishes the generated samples from the real ones. Experiments show that DECAF has comparable fairness to the state-of-the-art method FairGAN, but significantly outperforms it in terms of precision, recall, and AUROC. ", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "This paper proposes a novel approach for removing data biases that negatively affect fairness, yet generating realistic data using GAN techniques. There are some concerns on whether the generated data is realistic and whether DECAF should also be compared with weak supervision approaches.\n\nStrong points:\n\n* The unfairness mitigation method is principled and has theoretical guarantees. By removing edges from the DAG, one has a clear idea exactly what bias is being removed.\n\n* The DAG representation is general and can be used to express prominent group fairness measures.\n\n* The experiments show that DECAF outperforms the state-of-the-art method FairGAN among others.\n\nWeak points:\n\n* One concern is whether removing edges is too drastic and may result in unrealistic data. For example, Sec 5.2 mentions that surrogate variables can be sampled independently from a distribution or set to a fixed value. Let us say that we are using the Adult dataset and set all its gender values to male. From a practical point of view, wouldn't the dataset lose too much information? To answer this question, the authors should also show DECAF's discriminator performance because it may actually be able to distinguish generated versus real data better than say FairGAN's real/fake discriminator.\n\n* An alternative approach for fair data generation is to use weak supervision. In particular, the authors should cite and compare DECAF with Choi et al., \"Fair Generative Modeling via Weak Supervision\", ICML 2020. The idea is to exploit an additional small, unlabeled reference dataset as the supervision signal to generate unbiased data.\n\n* Some notions are used without definitions. In Sec. 3, please define \"independent causal mechanism\". In Sec. 4.3, define \"Markov boundary\", \"d-separation\", and \"explanatory feature\".\n\n* The experiments section looks a bit thin (accuracy and fairness experiments for two datasets), probably because many experiments are moved to the supplementary. In particular, the Adult dataset DAG is quite interesting and should be more visible. Also, it would be useful to see an ablation study that evaluates DECAF without some of its components (e.g., the discriminator). \n\n* In Sec. 6, please specify how the values of surrogate variables were chosen. There are some details in the supplementary, but it is not clear if the same settings were used in Sec. 6.\n \n=========\nThe author feedback addresses my concerns. I will keep my rating of 6. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes. Section 7 has a detailed discussion on limitations and societal impact.", "review_text": "", "extra_scores": {"ethical_concerns": "I do not see any ethical concerns.", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5"}, "extra_text": {}}]

Author rebuttal:

Meta-review: While the paper has initially some disagreement in score, it now arrives at a unanimous consensus by properly addressing all of the main concerns, in particular, regarding the limitation of the underlying assumption made in the paper, as well as providing more experimental results w.r.t. suggested baselines. I believe the paper is worth being published as a poster.
Decision: Accept (Poster)