DECAF:  Generating Fair Synthetic Data Using Causally-Aware Generative Networks

1 Introduction . Generative models are optimized to approximate the original data distribution as closely as 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-sensitive information [ 2 , 3 ] . We explore a much-less studied concept : synthetic data fairness . Motivation . Deployed machine learning models have been shown to reflect the bias of the data on which they are trained [ 4 , 5 , 6 , 7 , 8 ] . This has not only unfairly damaged the discriminated individuals but also society ’ s trust in machine learning as a 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 aim is related to the work of [ 17 ] : to generate fair synthetic data based on unfair data . Being able to generate fair data is important because end-users creating models based on publicly available data might be unaware they are inadvertently including ∗Equal contribution 35th Conference on Neural Information Processing Systems ( NeurIPS 2021 ) . 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 a biased dataset X , we are interested in learning a model G , that is able to generate an equivalent synthetic unbiased dataset X ′ with minimal loss of data utility . Furthermore , a 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 a causal standpoint because it provides an intuitive perspective on different definitions of fairness and discrimination [ 11 , 13 , 14 , 15 , 18 ] . We introduce DEbiasing CAusal Fairness ( DECAF ) , a 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 at inference-time through targeted ( biased ) edge removal . As a result , various datasets can be created for desired ( or evolving ) definitions of fairness . Contributions . We propose a framework of using causal knowledge for fair synthetic data generation . We make three main contributions : i ) DECAF , a causal GAN-based model for generating synthetic data , ii ) a flexible causal approach for modifying this model such that it 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 fairness/discrimination definitions used in literature while still maintaining high downstream utility of generated data . 2 Related Works . Here we focus on 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 to one another , we refer to Table 1 which presents all relevant related methods . Non-parametric generative modeling . The standard models for synthetic data generation are either based on VAEs [ 19 ] or GANs [ 2 , 3 , 20 , 21 ] . While these models are well known for their highly realistic synthetic data , they are unable to alter the synthetic data distribution to encourage fairness ( 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-derived ideas but are different in both method and aim ( i.e. , image generation ) . Fair data generation . In the bottom section of Table 1 , we present methods that , in some way , alter the training data of classifiers to adhere to a notion of fairness [ 10 , 11 , 16 , 17 , 22 , 23 ] . While these methods have proven successful , they lack some important features . For example , none of the related methods allow for post-hoc 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 a causal architecture for the generator , however their method is not as flexible—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 1 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 a 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 X ∈ X ⊆ Rd denote a random variable with distribution PX ( X ) , with protected attributes A ∈ A ⊂ X and target variable Y ∈ Y ⊂ X , let Ŷ denote a prediction of Y . Let the data be given by D = { x ( k ) } Nk=1 , where each x ( k ) ∈ D is a realization of X . We assume the data generating process can be represented by a directed acyclic graph ( DAG ) —such that the generation of features can be written as a structural equation model ( SEM ) [ 27 ] —and that this DAG is causally sufficient . Let Xi denote the ith feature in X with causal parents Pa ( Xi ) ⊂ { Xj : j 6= i } , the SEM is given by : Xi = fi ( Pa ( Xi ) , Zi ) , ∀i ( 1 ) where { Zi } di=1 are independent random noise variables , that is Pa ( Zi ) = ∅ , ∀i . Note that each fi is a deterministic function that places all randomness of the conditional P ( Xi|Pa ( Xi ) ) in the respective noise variable , Zi . 4 Fairness of Synthetic Data . Algorithmic fairness is 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 [ 29 ] , which is a generalization of the two . In Appendix C we discuss how the ideas in this section transfer to other independence-based definitions [ 30 ] . Throughout this section , we separate Y from X by defining X̄ = X\Y , and we will write X ← X̄ for ease of notation . 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 7→ Ŷ is fair iff protected attributes A are not explicitly used by f to predict Ŷ . 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 is commonly used , it might result in indirect discrimination : covariates that influence the prediction Ŷ 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 Ŷ is fair iff A ⊥⊥ Ŷ , i.e . ∀a , a′ : P ( Ŷ |A = a ) = P ( Ŷ |A = a′ ) . 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 to unresolved discrimination [ 14 ] . The idea is that we do not allow indirect discrimination unless it runs through explanatory factors R ⊂ X . For example , in Simpson ’ s paradox [ 33 ] there seems to be a 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 Ŷ is fair iff A ⊥⊥ Ŷ |R , i.e . ∀r , a , a′ : P ( Ŷ |R = r , A = a ) = P ( Ŷ |R = r , A = a′ ) . CF generalizes FTU and DP Note that conditional fairness is a generalization of FTU and DP , by setting R = X\A and R = ∅ , respectively . In Appendix C we elaborate on the connection between these , and more , definitions . 4.2 Synthetic data fairness . Algorithmic definitions can be extended to distributional fairness for synthetic data . Let P ( X ) , P ′ ( X ) be probability distributions with protected attributes A ⊂ X and labels Y ⊂ X . Let I ( A , Y ) be a definition of algorithmic fairness ( e.g. , FTU ) . Note , that under CF , I ( A , Y ) is a function of R as well . We propose ( I ( A , Y ) , P ) -fairness of distribution P ′ ( X ) : Definition 4 . ( Distributional fairness ) A probability distribution P ′ ( X ) is ( I ( A , Y ) , P ) -fair , iff the optimal predictor Ŷ = f∗ ( X ) of Y trained on P ′ ( X ) satisfies I ( A , Y ) when evaluated on P ( X ) . In other words , when we train a predictor on ( I ( A , Y ) , P ) -fair distribution P ′ ( X ) , we can only reach maximum performance if our model is fair . Note the explicit reference to P ( X ) , the distribution on which fairness is evaluated , which does not need to coincide with P ′ ( X ) . This is a 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 it 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 a distributional shift . By extension , we define synthetic data as ( I ( A , Y ) , P ) -fair , iff it is sampled from an ( I ( A , Y ) , P ) - fair distribution . Defining synthetic data as fair w.r.t . an optimal predictor is especially useful when we want to publish a dataset and do not trust end-users to consider anything but performance.2 Choosing P ( X ) . 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 a 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 is the setting where P ( X ) corresponds to the original data distribution PX ( X ) that contains unfairness . In this scenario , we construct P ′ ( X ) by learning PX ( X ) and removing the unfair characteristics . The data from P ′ ( X ) can be published online , and models trained on this data can be deployed fairly in real-life scenarios where data follows PX ( X ) . Unless otherwise stated , henceforth , we assume P ( X ) = PX ( X ) .

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.