Developing classification algorithms that are fair with respect to sensitive attributes of the data is an important problem due to the increased deployment of classification algorithms in societ al contexts. Several recent works have focused on studying classification with respect to specific fairness metrics, modeled the corresponding fair classification problem as constrained optimization problems, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which there are no fair classifiers with theoretical guarantees; primarily because the resulting optimization problem is non-convex. The main contribution of this paper is a meta-algorithm for classification that can take as input a general class of fairness constraints with respect to multiple non-disjoint and multi-valued sensitive attributes, and which comes with provable guarantees. In particular, our algorithm can handle non-convex "linear fractional" constraints (which includes fairness constraints such as predictive parity) for which no prior algorithm was known. Key to our results is an algorithm for a family of classification problems with convex constraints along with a reduction from classification problems with linear fractional constraints to this family. Empirically, we observe that our algorithm is fast, can achieve near-perfect fairness with respect to various fairness metrics, and the loss in accuracy due to the imposed fairness constraints is often small.
Another approach is to propose other fairness metrics as a proxy of statistical parity or equalized odds, e.g., @cite_38 @cite_31 @cite_48 . @cite_38 @cite_31 proposed a covariance-type constraint for statistical parity and equalized odds. The third approach post-processes a baseline classifier by shifting the decision boundary (can be different for different groups), e.g., @cite_3 @cite_32 @cite_54 @cite_50 @cite_39 @cite_22 . These approaches modify the constrained classification problem.
@cite_38 @cite_22 @cite_48 @cite_54 @cite_32 @cite_3 @cite_39 @cite_50 @cite_31
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We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability (arXiv:1104.3913), which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. This is intended to represent the interventions of a regulator who "knows unfairness when he sees it" but nevertheless cannot enunciate a quantitative fairness metric over individuals. Our main result is an algorithm in the adversarial context setting that has a number of fairness violations that depends only logarithmically on @math , while obtaining an optimal @math regret bound to the best fair policy. Motivated by settings in which predictive models may be required to be non-discriminatory with respect to certain attributes (such as race), but even collecting the sensitive attribute may be forbidden or restricted, we initiate the study of fair learning under the constraint of differential privacy. We design two learning algorithms that simultaneously promise differential privacy and equalized odds, a 'fairness' condition that corresponds to equalizing false positive and negative rates across protected groups. Our first algorithm is a private implementation of the equalized odds post-processing approach of [, 2016]. This algorithm is appealingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as a form of 'disparate treatment'. Our second algorithm is a differentially private version of the oracle-efficient in-processing approach of [, 2018] that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem. This algorithm is more complex but need not have access to protected group membership at test time. We identify new tradeoffs between fairness, accuracy, and privacy that emerge only when requiring all three properties, and show that these tradeoffs can be milder if group membership may be used at test time. We conclude with a brief experimental evaluation. The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier across these groups. Constraints of this form are susceptible to intentional or inadvertent "fairness gerrymandering", in which a classifier appears to be fair on each individual group, but badly violates the fairness constraint on one or more structured subgroups defined over the protected attributes. We propose instead to demand statistical notions of fairness across exponentially (or infinitely) many subgroups, defined by a structured class of functions over the protected attributes. This interpolates between statistical definitions of fairness and recently proposed individual notions of fairness, but raises several computational challenges. It is no longer clear how to audit a fixed classifier to see if it satisfies such a strong definition of fairness. We prove that the computational problem of auditing subgroup fairness for both equality of false positive rates and statistical parity is equivalent to the problem of weak agnostic learning, which means it is computationally hard in the worst case, even for simple structured subclasses. We then derive two algorithms that provably converge to the best fair classifier, given access to oracles which can solve the agnostic learning problem. The algorithms are based on a formulation of subgroup fairness as a two-player zero-sum game between a Learner and an Auditor. Our first algorithm provably converges in a polynomial number of steps. Our second algorithm enjoys only provably asymptotic convergence, but has the merit of simplicity and faster per-step computation. We implement the simpler algorithm using linear regression as a heuristic oracle, and show that we can effectively both audit and learn fair classifiers on real datasets. This paper studies two-class (or binary) classification of elements X in R k that allows for a reject option. Based on n independent copies of the pair of random variables (X,Y ) with X 2 R k and Y 2 0,1 , we consider classifiers f(X) that render three possible outputs: 0, 1 and R. The option R expresses doubt and is to be used for few observations that are hard to classify in an automatic way. Chow (1970) derived the optimal rule minimizing the risk P f(X) 6 Y, f(X) 6 R + dP f(X) = R . This risk function subsumes that the cost of making a wrong decision equals 1 and that of utilizing the reject option is d. We show that the classification problem hinges on the behavior of the regression function (x) = E(Y |X = x) near d and 1 d. (Here d 2 [0,1 2] as the other cases turn out to be trivial.) Classification rules can be categorized into plug-in estimators and empirical risk minimizers. Both types are considered here and we prove that the rates of convergence of the risk of any estimate depends on P | (X) d| + P | (X) (1 d)| and on the quality of the estimate for or an appropriate measure of the size of the class of classifiers, in case of plug-in rules and empirical risk minimizers, respectively. We extend the mathematical framework even further by dierentiating between costs associated with the two possible errors: predicting f(X) = 0 whilst Y = 1 and predicting f(X) = 1 whilst Y = 0. Such situations are common in, for instance, medical studies where misclassifying a sick patient as healthy is worse than the opposite. The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. However, the existing notions of fairness, based on parity (equality) in treatment or outcomes for different social groups, tend to be quite stringent, limiting the overall decision making accuracy. In this paper, we draw inspiration from the fair-division and envy-freeness literature in economics and game theory and propose preference-based notions of fairness -- given the choice between various sets of decision treatments or outcomes, any group of users would collectively prefer its treatment or outcomes, regardless of the (dis)parity as compared to the other groups. Then, we introduce tractable proxies to design margin-based classifiers that satisfy these preference-based notions of fairness. Finally, we experiment with a variety of synthetic and real-world datasets and show that preference-based fairness allows for greater decision accuracy than parity-based fairness. Nearest neighbour classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions. We propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods. We determine the local decision boundaries from centroid information, and then shrink neighbourhoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighbourhood-based classifier can be employed, using the modified neighbourhoods. The posterior probabilities tend to be more homogeneous in the modified neighbourhoods. We also propose a method for global dimension reduction, that combines local dimension information. In a number of examples, the methods demonstrate the potential for substantial improvements over nearest neighbour classification. Performance metrics for binary classification are designed to capture tradeoffs between four fundamental population quantities: true positives, false positives, true negatives and false negatives. Despite significant interest from theoretical and applied communities, little is known about either optimal classifiers or consistent algorithms for optimizing binary classification performance metrics beyond a few special cases. We consider a fairly large family of performance metrics given by ratios of linear combinations of the four fundamental population quantities. This family includes many well known binary classification metrics such as classification accuracy, AM measure, F-measure and the Jaccard similarity coefficient as special cases. Our analysis identifies the optimal classifiers as the sign of the thresholded conditional probability of the positive class, with a performance metric-dependent threshold. The optimal threshold can be constructed using simple plug-in estimators when the performance metric is a linear combination of the population quantities, but alternative techniques are required for the general case. We propose two algorithms for estimating the optimal classifiers, and prove their statistical consistency. Both algorithms are straightforward modifications of standard approaches to address the key challenge of optimal threshold selection, thus are simple to implement in practice. The first algorithm combines a plug-in estimate of the conditional probability of the positive class with optimal threshold selection. The second algorithm leverages recent work on calibrated asymmetric surrogate losses to construct candidate classifiers. We present empirical comparisons between these algorithms on benchmark datasets. In this paper, we investigate how to modify the naive Bayes classifier in order to perform classification that is restricted to be independent with respect to a given sensitive attribute. Such independency restrictions occur naturally when the decision process leading to the labels in the data-set was biased; e.g., due to gender or racial discrimination. This setting is motivated by many cases in which there exist laws that disallow a decision that is partly based on discrimination. Naive application of machine learning techniques would result in huge fines for companies. We present three approaches for making the naive Bayes classifier discrimination-free: (i) modifying the probability of the decision being positive, (ii) training one model for every sensitive attribute value and balancing them, and (iii) adding a latent variable to the Bayesian model that represents the unbiased label and optimizing the model parameters for likelihood using expectation maximization. We present experiments for the three approaches on both artificial and real-life data. We study binary classification in the presence of class-conditional random noise, where the learner gets to see labels that are flipped independently with some probability, and where the flip probability depends on the class. Our goal is to devise learning algorithms that are efficient and statistically consistent with respect to commonly used utility measures. In particular, we look at a family of measures motivated by their application in domains where cost-sensitive learning is necessary (for example, when there is class imbalance). In contrast to most of the existing literature on consistent classification that are limited to the classical 0-1 loss, our analysis includes more general utility measures such as the AM measure (arithmetic mean of True Positive Rate and True Negative Rate). For this problem of cost-sensitive learning under class-conditional random noise, we develop two approaches that are based on suitably modifying surrogate losses. First, we provide a simple unbiased estimator of any loss, and obtain performance bounds for empirical utility maximization in the presence of i.i.d. data with noisy labels. If the loss function satis_es a simple symmetry condition, we show that using unbiased estimator leads to an efficient algorithm for empirical maximization. Second, by leveraging a reduction of risk minimization under noisy labels to classification with weighted 0-1 loss, we suggest the use of a simple weighted surrogate loss, for which we are able to obtain strong utility bounds. This approach implies that methods already used in practice, such as biased SVM and weighted logistic regression, are provably noise-tolerant. For two practically important measures in our family, we show that the proposed methods are competitive with respect to recently proposed methods for dealing with label noise in several benchmark data sets. Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in the data through random projections in a fair'' subspace. We apply this method to densest subgraph and @math -means. For densest subgraph, our approach based on fair projections allows to recover both theoretically and empirically an almost optimal, fair, dense subgraph hidden in the input data. We also show that, under the small set expansion hypothesis, approximating this problem beyond a factor of @math is NP-hard and we show a polynomial time algorithm with a matching approximation bound. We further apply our method to @math -means. In a previous paper, [NIPS 2017] showed that problems such as @math -means can be approximated up to a constant factor while ensuring that none of two protected class (e.g., gender, ethnicity) is disparately impacted. We show that fair projections generalize the concept of fairlet introduced by to any number of protected attributes and improve empirically the quality of the resulting clustering. We also present the first constant-factor approximation for an arbitrary number of protected attributes thus settling an open problem recently addressed in several works. We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our approach. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches. Recently, the following discrimination aware classification problem was introduced: given a labeled dataset and an attribute B, find a classifier with high predictive accuracy that at the same time does not discriminate on the basis of the given attribute B. This problem is motivated by the fact that often available historic data is biased due to discrimination, e.g., when B denotes ethnicity. Using the standard learners on this data may lead to wrongfully biased classifiers, even if the attribute B is removed from training data. Existing solutions for this problem consist in “cleaning away” the discrimination from the dataset before a classifier is learned. In this paper we study an alternative approach in which the non-discrimination constraint is pushed deeply into a decision tree learner by changing its splitting criterion and pruning strategy. Experimental evaluation shows that the proposed approach advances the state-of-the-art in the sense that the learned decision trees have a lower discrimination than models provided by previous methods, with little loss in accuracy. We analyze the problem of learning a single user's preferences in an active learning setting, sequentially and adaptively querying the user over a finite time horizon. Learning is conducted via choice-based queries, where the user selects her preferred option among a small subset of offered alternatives. These queries have been shown to be a robust and efficient way to learn an individual's preferences. We take a parametric approach and model the user's preferences through a linear classifier, using a Bayesian prior to encode our current knowledge of this classifier. The rate at which we learn depends on the alternatives offered at every time epoch. Under certain noise assumptions, we show that the Bayes-optimal policy for maximally reducing entropy of the posterior distribution of this linear classifier is a greedy policy, and that this policy achieves a linear lower bound when alternatives can be constructed from the continuum. Further, we analyze a different metric called misclassification error, proving that the performance of the optimal policy that minimizes misclassification error is bounded below by a linear function of differential entropy. Lastly, we numerically compare the greedy entropy reduction policy with a knowledge gradient policy under a number of scenarios, examining their performance under both differential entropy and misclassification error. This paper deals with Bayesian selection of models that can be specified using inequality constraints among the model parameters. The concept of encompassing priors is introduced, that is, a prior distribution for an unconstrained model from which the prior distributions of the constrained models can be derived. It is shown that the Bayes factor for the encompassing and a constrained model has a very nice interpretation: it is the ratio of the proportion of the prior and posterior distribution of the encompassing model in agreement with the constrained model. It is also shown that, for a specific class of models, selection based on encompassing priors will render a virtually objective selection procedure. The paper concludes with three illustrative examples: an analysis of variance with ordered means; a contingency table analysis with ordered odds-ratios; and a multilevel model with ordered slopes. 1 Inequality constrained statistical models Researchers often have one or more (competing) theories about their field of research. Consider, for example, theories about the effect of behavioral therapy versus medication for children with an attention deficit disorder (ADD). Some researchers in this area believe medication is the only effective treatment for ADD, some believe strongly in behavioral therapy, and others may expect an additive effect of both therapies. To test or compare the plausibility of these theories they need to be translated into statistical models. Subsequently, empirical data can be used to determine which model is best. Inequality constraints on model parameters can be useful in the specification of statistical models. This paper deals with competing models that have the same parameter vector, but in one or more of the models parameters are subjected to inequality constraints. To continue the example, consider an experiment where children with ADD are randomly assigned to one of four conditions: no treatment (1), behavioral therapy (2), medication (3), and behavioral therapy plus medication (4). Let the outcome In this paper, we introduce the Fairness GAN, an approach for generating a dataset that is plausibly similar to a given multimedia dataset, but is more fair with respect to protected attributes in allocative decision making. We propose a novel auxiliary classifier GAN that strives for demographic parity or equality of opportunity and show empirical results on several datasets, including the CelebFaces Attributes (CelebA) dataset, the Quick, Draw! dataset, and a dataset of soccer player images and the offenses they were called for. The proposed formulation is well-suited to absorbing unlabeled data; we leverage this to augment the soccer dataset with the much larger CelebA dataset. The methodology tends to improve demographic parity and equality of opportunity while generating plausible images. With the spread of data mining technologies and the accumulation of social data, such technologies and data are being used for determinations that seriously affect people's lives. For example, credit scoring is frequently determined based on the records of past credit data together with statistical prediction techniques. Needless to say, such determinations must be socially and legally fair from a viewpoint of social responsibility, namely, it must be unbiased and nondiscriminatory in sensitive features, such as race, gender, religion, and so on. Several researchers have recently begun to attempt the development of analysis techniques that are aware of social fairness or discrimination. They have shown that simply avoiding the use of sensitive features is insufficient for eliminating biases in determinations, due to the indirect influence of sensitive information. From a privacy-preserving viewpoint, this can be interpreted as hiding sensitive information when classification results are observed. In this paper, we first discuss three causes of unfairness in machine learning. We then propose a regularization approach that is applicable to any prediction algorithm with probabilistic discriminative models. We further apply this approach to logistic regression and empirically show its effectiveness and efficiency. With the spread of data mining technologies and the accumulation of social data, such technologies and data are being used for determinations that seriously affect individuals' lives. For example, credit scoring is frequently determined based on the records of past credit data together with statistical prediction techniques. Needless to say, such determinations must be nondiscriminatory and fair in sensitive features, such as race, gender, religion, and so on. Several researchers have recently begun to attempt the development of analysis techniques that are aware of social fairness or discrimination. They have shown that simply avoiding the use of sensitive features is insufficient for eliminating biases in determinations, due to the indirect influence of sensitive information. In this paper, we first discuss three causes of unfairness in machine learning. We then propose a regularization approach that is applicable to any prediction algorithm with probabilistic discriminative models. We further apply this approach to logistic regression and empirically show its effectiveness and efficiency. Automated data-driven decision making systems are increasingly being used to assist, or even replace humans in many settings. These systems function by learning from historical decisions, often taken by humans. In order to maximize the utility of these systems (or, classifiers), their training involves minimizing the errors (or, misclassifications) over the given historical data. However, it is quite possible that the optimally trained classifier makes decisions for people belonging to different social groups with different misclassification rates (e.g., misclassification rates for females are higher than for males), thereby placing these groups at an unfair disadvantage. To account for and avoid such unfairness, in this paper, we introduce a new notion of unfairness, disparate mistreatment, which is defined in terms of misclassification rates. We then propose intuitive measures of disparate mistreatment for decision boundary-based classifiers, which can be easily incorporated into their formulation as convex-concave constraints. Experiments on synthetic as well as real world datasets show that our methodology is effective at avoiding disparate mistreatment, often at a small cost in terms of accuracy. We study the problem of fair allocation for indivisible goods. We use the the maxmin share paradigm introduced by Budish as a measure for fairness. Procacciafirst (EC'14) were first to investigate this fundamental problem in the additive setting. In contrast to what real-world experiments suggest, they show that a maxmin guarantee (1- @math allocation) is not always possible even when the number of agents is limited to 3. While the existence of an approximation solution (e.g. a @math - @math allocation) is quite straightforward, improving the guarantee becomes subtler for larger constants. Procaccia provide a proof for existence of a @math - @math allocation and leave the question open for better guarantees. Our main contribution is an answer to the above question. We improve the result of ! to a @math factor in the additive setting. The main idea for our @math - @math allocation method is clustering the agents. To this end, we introduce three notions and techniques, namely reducibility, matching allocation, and cycle-envy-freeness, and prove the approximation guarantee of our algorithm via non-trivial applications of these techniques. Our analysis involves coloring and double counting arguments that might be of independent interest. One major shortcoming of the current studies on fair allocation is the additivity assumption on the valuations. We alleviate this by extending our results to the case of submodular, fractionally subadditive, and subadditive settings. More precisely, we give constant approximation guarantees for submodular and XOS agents, and a logarithmic approximation for the case of subadditive agents. Furthermore, we complement our results by providing close upper bounds for each class of valuation functions. Finally, we present algorithms to find such allocations for additive, submodular, and XOS settings in polynomial time. We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses.