Generative Fairness Teaching

1 INTRODUCTION . Automated learning systems are ubiquitous across a wide variety of sectors . Such systems can be used in many sensitive environments to make important and even life-changing decisions . Traditionally , decisions are made primary by human and the basis are usually highly regulated . For example in the Equal Credit Opportunity ACts ( ECOA ) , incorporating attributes such as race , color , or sex into credit lending decisions are illegal in United States ( Mehrabi et al. , 2019 ) . As more and more of this process nowadays is implemented by automated learning systems instead , algorithmic fairness becomes a topic of paramount importance . Lending ( Hardt et al. , 2016 ) , hiring ( Alder & Gilbert , 2006 ) , and educational rights ( Kusner et al. , 2017 ) are examples where gender or race biased decisions from automatic systems can have serious consequences . Even for more mechanical tasks such as image classification ( Buolamwini & Gebru , 2018 ) , image captioning ( Hendricks et al. , 2018 ) , word embedding learning ( Garg et al. , 2018 ; Bolukbasi et al. , 2016 ) , and named co-reference resolution ( Zhao et al. , 2018 ) , algorithmic discrimination can be a major concern . As the society relies more and more on such automated systems , algorithmic fairness becomes a pressing issue . Although much of the focus of developing automated learning systems has been on the performance , it is important to take fairness into consideration while designing and deploying the systems . Unfortunately , state-of-the-art automated systems are usually data driven , which makes it more likely to inherit or even amplify the biases rooted in a dataset . This is an especially serious issue for deep learning and gradient based models , which can easily fit itself into the biased patterns of the dataset . For example , in a dataset with very few female candidates being labeled as hired in a job candidate prediction task , models might choose to give unfavorable predictions to qualified female candidates due to their under-representations in the training data . If deployed , such a biased predictor will deprive minority groups from acquiring the same opportunities as the others . Much of the work in the domain of machine learning fairness has been focusing exclusively on leveraging knowledge from samples in a dataset . One straightforward way is to adjust the distributions of the training data through pre-processing . In the job candidate prediction example above , this means that we can either down-sample the majority class or up-sample the minority ones ( Kamiran & Calders , 2012 ) . Another family of fairness methods aims at matching the model performance on the majority class to that of the minority ones during training by using one of the fairness criteria ( Gajane & Pechenizkiy , 2017 ) . Some examples of such methods includes adding regularizations ( Kamishima et al. , 2012 ) or applying adversarial learning ( Madras et al. , 2018a ) . One issue with these approaches is that in many cases minority groups might be heavily under-represented in the dataset . Model training with fairness constraints will typically give up much of the performance ad- vantages ( e.g. , prediction accuracies ) in favor of the fairness metrics . Methods concentrate on solely on a dataset will often find themselves difficult to maintain a good performance - fairness trade-off . One way to make models learn beyond the dataset is to take advantage of causal reasoning ( Pearl et al. , 2009 ) , which borrows knowledge from external structures often formulated as a causal graph . Counterfactual Fairness ( Kusner et al. , 2017 ) and Causal Fairness ( Kilbertus et al. , 2017 ) are examples of such approaches . One unique characteristic of causal fairness is the fact that they need to be built based on a causal graph . And because those metrics are usually optimized and evaluated their own objective , which involves a causal graph , it ’ s not clear how that added knowledge can be used to benefit other more commonly used fairness criteria such as Demographic Parity and Equalized Odds . Although it is possible to create causal structures that subsume conditional independencies in order to benefit DP or EO , we will need those structure information to be known in advance and we will have to derive one such structure for each metric we find . This is , what we believed , a significant limitation of the current causal methods which we aim to improve . In this paper , we propose a generative approach for fairness training that is capable of leveraging both real data and “ counterfactual data ” generated from a causal graph . The counterfactual data is generated in a way that alters the sensitive attribute while keeping other latent factors unchanged . We formulate such generative model using a novel combination of adversarial training with mutual information regularization . Next , the two types of data are organized by an architecture called the teacher , which dynamically determines the proportion of real and counterfactual samples to train a particular model . Our model - Generative Fairness Teacher ( GFT ) can be used to improve an arbitrary fairness criteria based on need . Our experimental results indicate that we are able to take advantage of the counterfactual generative model and make it able to achieve a significantly better model fairness on a wide range of datasets across models . we are able to improve upon models with different levels of biases . 2 BACKGROUND . We provides a basic overview for the foundations of our method . Here we assume X to be the input features , while A being the set of sensitive features . We define Y the be favorable outcome and Ŷ to be the models ’ prediction of the favorable outcome given the features . The core idea of Fairness in machine learning is to distribute those favorable outcomes evenly across each of the sensitive group A . 2.1 FORMAL FAIRNESS CRITERIA . There has been many existing work on fairness focusing on studying criteria to achieve algorithmic fairness . A straightforward way to define fairness is Demographic Parity Madras et al . ( 2018a ) . In Demographic Parity , the chances of allocating the favorable outcomes Ŷ is the same across sensitive groupsA . Under that definition , the predictive variable Ŷ is independent withA , making predictions free from discrimination against sensitive groups . Note that even thoughA takes the form of a binary variable , we can easily extend the definition into the case of multiple values . Definition 1 Demographic Parity P ( Ŷ |X = x , A = a ) = P ( Ŷ |X = x , A = a′ ) ( 1 ) Other fairness criteria that are built based on input features includes include Fairness Through Unawareness Gajane & Pechenizkiy ( 2017 ) , and Individual Fairness Kusner et al . ( 2017 ) . More recently , Hardt et al . argued that criteria that only takes into account sample features making it difficult for the algorithms to allocate favorable outcomes to the actual qualified samples in both the minority and the majority groups . Such an observation leading to a new fairness criteria called Equalized Odds ( and its special case Equal Opportunity ) Hardt et al . ( 2016 ) , where the fairness statement includes a condition on target variable Y . Definition 2 Equalized Odds P ( Ŷ = 1|X = x , A = a , Y = y ) = P ( Ŷ = 1|X = x , A = a′ , Y = y ) ( 2 ) 3 CAUSAL MODELS AND COUNTERFACTUAL EXAMPLES . A causal model Pearl et al . ( 2000 ) is defined over a triple ( U , V , F ) where V is a set of observed variables and U being a set of latent background variables . F is defined to be a set of equations for each variable in V , Vi = fi ( pai , Upai ) . Here pai refers to the parent of i in a causal graph . One importance concept in causal reasoning is intervention , in which case we substitute the variable of certain equation vi = v. We define a counterfactual example to be a synthesized sample generated from an existing data X by manipulating its sensitive feature from a to a′ . Here we assume that both the real sample X and the counterfactual sample X̂A←a′ are generated from a latent code U . Definition 3 Counterfactual Example X̂A←a′ ( U ) |X , a ( 3 ) 3.1 COMMON TECHNIQUES FOR FAIRNESS . Depending on when the fairness criteria are applied , methods for achieving fairness can be categorized as pre-processing , in-processing and post-processing Mehrabi et al . ( 2019 ) . In-processing Techniques . In-processing techniques apply fairness criteria during the training . Common techniques including fairness regularizer Kamishima et al . ( 2012 ) and adversarial training Madras et al . ( 2018a ) . Other methods fall into this category including the reduction based method Agarwal et al . ( 2018 ) and the more traditional discrimination approach in data miningHajian & Domingo-Ferrer ( 2012 ) . Our implementation applies in-processing techniques although our framework does not deal with in-processing methods directly . Pre-processing Techniques . Pre-processing methods applies to the models before the actual training happens . Methods fall into this category are almost exclusively data processing techniques that aims at making the dataset free from biases . Re-sampling and re-weighting are two common techniques of pre-processing techniques for fairness . Calmon et al . ( 2017 ) ; Kamiran & Calders ( 2012 ) ; Agarwal et al . ( 2018 ) . Other techniques include that repairs biases in a database Salimi et al . ( 2019 ) . Our method is closely related to the pre-processing techniques because from the perspective of the student model our teacher model can be viewed as a data pre-processor . Post-processing Techniques . When fairness adjustments are applied after the training is finished , techniques are called post-processing methods . Post-processing methods can be used to adapt models with all kinds of biases levels into a fair model Madras et al . ( 2018b ) . Other recently proposed including the method to model fairness as a score transformation problem Wei et al . ( 2019 ) and methods enforces Independence between sensitive features and model outcomes through Wasserstein-1 distances Jiang et al . ( 2020 ) Our approach is closely related to the post-processing technique as our teacher model can work with an arbitrarily biased student model . 4 GENERATIVE FAIRNESS TEACHING . In this section , we propose a teaching framework for training a student model that is able to work with a wide range of fairness criteria . We first present the overview of our approach in section 4.1 . Then in section 4.2 , we elaborate a novel generative model that can create “ counterfactual examples ” . In section 4.4 we will show how to train such a teacher policy with the given student model and counterfactual generative model . 4.1 FAIRNESS TEACHING FRAMEWORK . Given a training dataset Dtrain = { ( X = xi , Y = yi , A = ai ) } |Dtrain|i=1 , where X and Y are observed features and label , respectively , and A is some sensitive attribute , we are interested in learning a predictive model pθ ( Y |X ) that is parameterized by θ , such that it maximizes the reward on the validation set : R ( θ ) = E ( x , y ) ∼Dvalid log pθ ( y|x ) − λfcFC ( pθ ( Y |X ) , Dvalid ) ( 4 ) Algorithm 1 Generative Teaching Procedure 1 : Input : initial student model pθ0 ( Y |X ) , counterfactual generator p̂ ( X̂ ) 2 : Input : dataset D , Teacher policy πψ 3 : for t← 1 to episode length T do 4 : Sample a minibatch D′ = { di = [ xi , yi , ai ] } Mi=1 ∼ D. 5 : Get counterfactual data D̂′ = { d̂i = [ x̂i ∼ p̂ ( ·|X = xi , A = ai ) , yi , a′i ] } for each di ∈ D′ . 6 : Get current student ’ s state s = S ( D′ , pθt−1 ( Y |X ) ) using Eq 11 . 7 : Obtain decision at ∼ πψ ( s ) , and get D̃ = { di ∈ D′|a ( i ) t = 0 } ⋃ { d̂i ∈ D̂′|a ( i ) t = 1 } . 8 : Update student : θt = θt−1 + η∇θ=θt−1 1|D̃| ∑ ( x , y ) ∈D̃ log pθ ( y|x ) 9 : end for 10 : Return : updated student model pθT ( Y |X ) where FC ( · , · ) stands for the evaluation metric under certain fairness requirement , such as equalized odds . This objective tries to balance between the generalization error and the fairness constraint , which is controlled by the hyperparameter λfc . In our teaching framework , we will teach a student predictive model pθ ( Y |X ) to minimize Eq 4 . Our teacher model πψ is responsible for providing proper data samples for the student at each step of optimization to achieve this goal . In most teaching frameworks , the teacher is only responsible for selecting proper samples from existing dataset . However , due to the potential bias in the dataset , such assumption is too limited to achieve the fairness requirement . Recall the definition of counterfactual example in Eq 3 . Given a tuple of ( U , X = x , A = a ) , changingA byA← a′ while keeping U fixed will also changeX . Thus the change to the predictive distribution p ( ŶA←a′ ( U ) |x , a ) depends on two aspects : 1 ) the predictive model pθ ( Y |X ) , and 2 ) a counterfactual generative model p̂ ( X̂ ) : = p ( X̂A←a′ ( U ) |X = x , A = a ) . Suppose we have the model p̂ ( X̂ ) ready , then it would be possible to regulate pθ ( Y |X ) by generate counterfactual samples during training . Given the teacher model πψ and the counterfactual generative model p̂ ( X̂ ) , we are ready to present our iterative teaching approach for learning pθ ( Y |X ) in algorithm 1 . At each teaching stage , the teacher will make binary decisions on using 1 ) the sample selection from the given dataset Dtrain , or 2 ) the counterfactual data ( X̂ , Y , A = a′ ) coming from data sample ( X , Y , A = a ) ∈ Dtrain and altered by p̂ ( X̂ ) . The student will then use the selected samples to perform gradient update of θ . In the following sections , we will present how such counterfactual generative model p̂ ( X̂ ) are learned through teaching policy πψ . 4.2 LEARNING COUNTERFACTUAL GENERATOR p̂ ( X̂ ) To learn the counterfactual data distribution , we first need an understanding of the empirical data distribution . In next subsection , we first present our latent variable modeling of the data distribution :

Summary: This paper combines counterfactual modeling with adversarial training for fair machine learning tasks. For a given fairness metric chosen from a variety of canonical examples, the method ensures fairness by augmenting the data with counterfactual examples during training. The approach has potential, which is best demonstrated on examples where the counterfactual data generation is interesting, like the CelebA data.