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.