We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong individual fairness. By varying the weight on the fairness regularizer, we can compute the efficient frontier of the accuracy-fairness trade-off on any given dataset, and we measure the severity of this trade-off via a numerical quantity we call the Price of Fairness (PoF). The centerpiece of our results is an extensive comparative study of the PoF across six different datasets in which fairness is a primary consideration.
In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via fair feature embedding (FKR-F$^2$E) in kernel space. Motivated by prior works on feature selection in kernel space and feature processing for fair machine learning, we propose to learn fair feature embedding functions that minimize demographic discrepancy of feature distributions in kernel space. Compared to the state-of-the-art fair kernel regression method…
Microsoft Research（微软研究院）；University of Minnesota（明尼苏达大学）
In this paper, we study the prediction of a real-valued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems \emph{fair regression}. We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined lev…
Shenzhen Research Institute of Big Data（深圳大数据研究院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Pennsylvania State University（宾夕法尼亚州立大学）
We study the fair regression problem under the notion of Mean Parity (MP) fairness, which requires the conditional mean of the learned function output to be constant with respect to the sensitive attributes. We address this problem by leveraging reproducing kernel Hilbert space (RKHS) to construct the functional space whose members are guaranteed to satisfy the fairness constraints. The proposed functional space suggests a closed-form solution for the fair regression problem that is naturally compatible with multiple sensitive attributes. Furthermore, by formulating the fairness-accuracy trade…
We present pairwise fairness metrics for ranking models and regression models that form analogues of statistical fairness notions such as equal opportunity, equal accuracy, and statistical parity. Our pairwise formulation supports both discrete protected groups, and continuous protected attributes. We show that the resulting training problems can be efficiently and effectively solved using existing constrained optimization and robust optimization techniques developed for fair classification. Experiments illustrate the broad applicability and trade-offs of these methods.
We initiate the study of fairness for ordinal regression. We adapt two fairness notions previously considered in fair ranking and propose a strategy for training a predictor that is approximately fair according to either notion. Our predictor has the form of a threshold model, composed of a scoring function and a set of thresholds, and our strategy is based on a reduction to fair binary classification for learning the scoring function and local search for choosing the thresholds. We provide generalization guarantees on the error and fairness violation of our predictor, and we illustrate the ef…
Most work in algorithmic fairness to date has focused on discrete outcomes, such as deciding whether to grant someone a loan or not. In these classification settings, group fairness criteria such as independence, separation and sufficiency can be measured directly by comparing rates of outcomes between subpopulations. Many important problems however require the prediction of a real-valued outcome, such as a risk score or insurance premium. In such regression settings, measuring group fairness criteria is computationally challenging, as it requires estimating information-theoretic divergences b…
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting on fewer samples). However, as we show, in some cases, the performance of a minority subgroup can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive subgroups. Motivated by these disparities, we propose new fairness criteria for selective regression …
Most fair regression algorithms mitigate bias towards sensitive sub populations and therefore improve fairness at group level. In this paper, we investigate the impact of such implementation of fair regression on the individual. More precisely, we assess the evolution of continuous predictions from an unconstrained to a fair algorithm by comparing results from baseline algorithms with fair regression algorithms for the same data points. Based on our findings, we propose a set of post-processing algorithms to improve the utility of the existing fair regression approaches.
International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术学院）
In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimization frameworks to obtain fair classifiers. Surrogates serve only as an upper bound to the actual constraints, and convexifying fairness constraints might be challenging. We propose a neural network-based framework, \emph{FNNC}, to achieve fairness while maintaining high accurac…
University of Alberta（阿尔伯塔大学）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Algorithmic fairness has received increased attention in socially sensitive domains. While rich literature on mean fairness has been established, research on quantile fairness remains sparse but vital. To fulfill great needs and advocate the significance of quantile fairness, we propose a novel framework to learn a real-valued quantile function under the fairness requirement of Demographic Parity with respect to sensitive attributes, such as race or gender, and thereby derive a reliable fair prediction interval. Using optimal transport and functional synchronization techniques, we establish th…
The University of Texas at Dallas（得克萨斯大学达拉斯分校）；Department of Computer Science（计算机科学系）
In this work, we develop a novel fairness learning approach for multi-task regression models based on a biased training dataset, using a popular rank-based non-parametric independence test, i.e., Mann Whitney U statistic, for measuring the dependency between target variable and protected variables. To solve this learning problem efficiently, we first reformulate the problem as a new non-convex optimization problem, in which a non-convex constraint is defined based on group-wise ranking functions of individual objects. We then develop an efficient model-training algorithm based on the framework…
University of Oxford（牛津大学）；Northampton University（北安普顿大学）
Fairness, through its many forms and definitions, has become an important issue facing the machine learning community. In this work, we consider how to incorporate group fairness constraints in kernel regression methods, applicable to Gaussian processes, support vector machines, neural network regression and decision tree regression. Further, we focus on examining the effect of incorporating these constraints in decision tree regression, with direct applications to random forests and boosted trees amongst other widespread popular inference techniques. We show that the order of complexity of me…
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Université Gustave Eiffel（古斯塔夫·埃菲尔大学）；University of Genoa（热那亚大学）；Istituto Italiano di Tecnologia（意大利技术研究院）；University College London（伦敦大学学院）
We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction. We establish a connection between fair regression and optimal transport theory, based on which we derive a close form expression for the optimal fair predictor. Specifically, we show that the distribution of this optimum is the Wasserstein barycenter of the distributions induced by the standard regression function o…
Though there is a growing body of literature on fairness for supervised learning, the problem of incorporating fairness into unsupervised learning has been less well-studied. This paper studies fairness in the context of principal component analysis (PCA). We first present a definition of fairness for dimensionality reduction, and our definition can be interpreted as saying that a reduction is fair if information about a protected class (e.g., race or gender) cannot be inferred from the dimensionality-reduced data points. Next, we develop convex optimization formulations that can improve the f…
NYU Grossman School of Medicine（纽约大学格罗斯曼医学院）；University of California, Irvine（加州大学欧文分校）
Despite recent advances in algorithmic fairness, methodologies for achieving fairness with generalized linear models (GLMs) have yet to be explored in general, despite GLMs being widely used in practice. In this paper we introduce two fairness criteria for GLMs based on equalizing expected outcomes or log-likelihoods. We prove that for GLMs both criteria can be achieved via a convex penalty term based solely on the linear components of the GLM, thus permitting efficient optimization. We also derive theoretical properties for the resulting fair GLM estimator. To empirically demonstrate the effi…
In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a …
In this paper, we take a first step towards answering the question of how to design fair machine learning algorithms that are robust to adversarial attacks. Using a minimax framework, we aim to design an adversarially robust fair regression model that achieves optimal performance in the presence of an attacker who is able to add a carefully designed adversarial data point to the dataset or perform a rank-one attack on the dataset. By solving the proposed nonsmooth nonconvex-nonconcave minimax problem, the optimal adversary as well as the robust fairness-aware regression model are obtained. For…
The applications of Artificial Intelligence (AI) surround decisions on increasingly many aspects of human lives. Society responds by imposing legal and social expectations for the accountability of such automated decision systems (ADSs). Fairness, a fundamental constituent of AI accountability, is concerned with just treatment of individuals and sensitive groups (e.g., based on sex, race). While many studies focus on fair learning and fairness testing for the classification tasks, the literature is rather limited on how to examine fairness in regression tasks. This work presents error parity a…
We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $ϕ_1 - ϕ_2$ for a choice of convex functions $ϕ_1, ϕ_2$. The method proceeds by estimating piecewise-liner convex functions, in a manner similar to max-affine regression, whose difference approximates the data. The choice of the function is regularised by a new seminorm over the class of DC functions that controls the $\ell_\infty$ Lipschitz constant of the estimate. The resulting methodolog…
Penalized Fair Regression for Multiple Groups in Chronic Kidney Disease
Department of Health Policy, Stanford University（健康政策系，斯坦福大学）；Stanford University（斯坦福大学）；Department of Epidemiology and Population Health, Stanford University（流行病学与人口健康系，斯坦福大学）
INRIA（法国国家信息与自动化研究所）；Ecole normale supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints corresponding to first-order stochastic dominance. We propose new discretization schemes that lead to simple and efficient algorithms based on zero-th, first, or higher order oracles; these algorithms also lead to improvements without isotonic constraints. Finally, our experiments show that non-convex loss functions can be much more robust to outliers for isoton…
Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation techniques to find a convex surrogate for the problem. Unfortunately, convex relaxations typically must be found on a problem-by-problem basis. Thus, providing a general-purpose strategy to estimate a convex relaxation would have a wide reaching impact. Here, we introduce Convex Relaxation Regression (CoRR), an approach for learning convex relaxations for a clas…
Intersectional Divergence: Measuring Fairness in Regression
Lucy Family Institute for Data \& Society, University of Notre Dame Notre Dame IN USA；Lucy Family Institute for Data \& Society, University of Notre Dame
Australian National University（澳大利亚国立大学）；Google（谷歌公司）
Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals in this regard over the past few years. Several of these, however, assume either binary sensitive features (thus precluding categorical or real-valued sensitive groups), or result in non-convex objectives (thus adversely affecting the optimisation landscape). In this paper, we propose a new definition of fairness that generalises some existing proposals, whi…
University of Pennsylvania（宾夕法尼亚大学）；Stanford University（斯坦福大学）；University of Washington（华盛顿大学）
We show how to take a regression function $\hat{f}$ that is appropriately ``multicalibrated'' and efficiently post-process it into an approximately error minimizing classifier satisfying a large variety of fairness constraints. The post-processing requires no labeled data, and only a modest amount of unlabeled data and computation. The computational and sample complexity requirements of computing $\hat f$ are comparable to the requirements for solving a single fair learning task optimally, but it can in fact be used to solve many different downstream fairness-constrained learning problems effi…
Quantile regression is a tool for learning conditional distributions. In this paper we study quantile regression in the setting where a protected attribute is unavailable when fitting the model. This can lead to "unfair'' quantile estimators for which the effective quantiles are very different for the subpopulations defined by the protected attribute. We propose a procedure for adjusting the estimator on a heldout sample where the protected attribute is available. The main result of the paper is an empirical process analysis showing that the adjustment leads to a fair estimator for which the t…
University of Arkansas（阿肯色大学）；University of Illinois（伊利诺伊大学）
Recent research on fair regression focused on developing new fairness notions and approximation methods as target variables and even the sensitive attribute are continuous in the regression setting. However, all previous fair regression research assumed the training data and testing data are drawn from the same distributions. This assumption is often violated in real world due to the sample selection bias between the training and testing data. In this paper, we develop a framework for fair regression under sample selection bias when dependent variable values of a set of samples from the traini…
Shanghai Jiao Tong University（上海交通大学）；Nanjing University of Science and Technology（南京理工大学）；KU Leuven（鲁汶大学）
In kernel methods, the kernels are often required to be positive definite, which restricts the use of many indefinite kernels. To consider those non-positive definite kernels, in this paper, we aim to build an indefinite kernel learning framework for kernel logistic regression. The proposed indefinite kernel logistic regression (IKLR) model is analysed in the Reproducing Kernel Kre\uın Spaces (RKKS) and then becomes non-convex. Using the positive decomposition of a non-positive definite kernel, the derived IKLR model can be decomposed into the difference of two convex functions. Accordingly, a…
Georgia Tech（佐治亚理工学院）；Google（谷歌）；Amazon Web Services（亚马逊云科技）；University of Washington（华盛顿大学）
We propose simple active sampling and reweighting strategies for optimizing min-max fairness that can be applied to any classification or regression model learned via loss minimization. The key intuition behind our approach is to use at each timestep a datapoint from the group that is worst off under the current model for updating the model. The ease of implementation and the generality of our robust formulation make it an attractive option for improving model performance on disadvantaged groups. For convex learning problems, such as linear or logistic regression, we provide a fine-grained ana…
Shanghai Tenth People's Hospital（上海市第十人民医院）；Tongji University（同济大学）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Jilin University（吉林大学）；The Ohio State University（俄亥俄州立大学）
Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset rather than the minimal margin of a few support vectors, is prone to achieve better generalization performance. However, the margin distribution support vector regression machines suffer difficulties resulted from solving a non-convex quadratic optimization, compared to the margin …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Department of Computer Science（计算机科学系）
Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy with a real-valued target is not entirely clear. In this paper, we characterize the inherent tradeoff between statistical parity and accuracy in the regression setting by providing a lower bound on the error of any fair regressor. Our lower bound is sharp, algorithm-independent, and admits a simple interpret…
Wasserstein projection distance for fairness testing of regression models
Department of Computer Science, University of British Columbia（计算机科学系，不列颠哥伦比亚大学）；Department of Pathology and Laboratory Medicine, University of British Columbia（病理学与实验室医学系，不列颠哥伦比亚大学）；Department of Statistics, University of British Columbia（统计学系，不列颠哥伦比亚大学）；BC Cancer Research, Part of Provincial Health Care Authority（BC癌症研究，省卫生保健机构的一部分）；Department of Mathematics, University of British Columbia（数学系，不列颠哥伦比亚大学）
Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems where the prediction is categorical, such as accepting or rejecting a loan application. This is in part because classification fairness measures are easily computed by comparing the rates of outcomes, leading to behaviours such as ensuring that the same fraction of eligible men are selected as eligible women. But such measures are computationally difficult to …
In this paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse regression and clustering with unknown binary labels. The corresponding optimization problem is combinatorial, but we propose a novel relaxation of it as an \emph{invex} optimization problem. To the best of our knowledge, this is the first invex relaxation for a combinatorial problem. We show that the inclusion of the debiasing/fairness constraint in our model …
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the covariates. The estimated linear combinations include all covariates, making results difficult to interpret and perhaps unnecessarily variable, particularly when the number of covariates is large. In this paper, we propose a convex formulation for fitting sparse sliced inverse regression in high dimensions. Our proposal estimates the subspace of the linear c…
Recent years have seen much research on fairness in machine learning. Here, mean difference (MD) or demographic parity is one of the most popular measures of fairness. However, MD quantifies not only discrimination but also explanatory bias which is the difference of outcomes justified by explanatory features. In this paper, we devise novel models, called FairCEEs, which remove discrimination while keeping explanatory bias. The models are based on estimators of causal effect utilizing propensity score analysis. We prove that FairCEEs with the squared loss theoretically outperform a naive MD co…
School of Social Sciences（社会科学学院）；University of Mannheim（曼海姆大学）；Department of Statistics（统计学系）；LMU Munich（慕尼黑大学）
Both industry and academia have made considerable progress in developing trustworthy and responsible machine learning (ML) systems. While critical concepts like fairness and explainability are often addressed, the safety of systems is typically not sufficiently taken into account. By viewing data-driven decision systems as socio-technical systems, we draw on the uncertainty in ML literature to show how fairML systems can also be safeML systems. We posit that a fair model needs to be an uncertainty-aware model, e.g. by drawing on distributional regression. For fair decisions, we argue that a sa…
University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Carnegie Mellon University（卡内基梅隆大学）
Developing classification methods with high accuracy that also avoid unfair treatment of different groups has become increasingly important for data-driven decision making in social applications. Many existing methods enforce fairness constraints on a selected classifier (e.g., logistic regression) by directly forming constrained optimizations. We instead re-derive a new classifier from the first principles of distributional robustness that incorporates fairness criteria into a worst-case logarithmic loss minimization. This construction takes the form of a minimax game and produces a parametri…
Centre for Social Research and Methods（社会研究与方法中心）；Australian National University（澳大利亚国立大学）
Counterfactual fairness is an approach to AI fairness that tries to make decisions based on the outcomes that an individual with some kind of sensitive status would have had without this status. This paper proposes Double Machine Learning (DML) Fairness which analogises this problem of counterfactual fairness in regression problems to that of estimating counterfactual outcomes in causal inference under the Potential Outcomes framework. It uses arbitrary machine learning methods to partial out the effect of sensitive variables on nonsensitive variables and outcomes. Assuming that the effects of…
University of Genova（热那亚大学）；Amazon Web Services（亚马逊云科技）；Istituto Italiano di Tecnologia（意大利理工学院）；University College London（伦敦大学学院）
We tackle the problem of algorithmic fairness, where the goal is to avoid the unfairly influence of sensitive information, in the general context of regression with possible continuous sensitive attributes. We extend the framework of fair empirical risk minimization to this general scenario, covering in this way the whole standard supervised learning setting. Our generalized fairness measure reduces to well known notions of fairness available in literature. We derive learning guarantees for our method, that imply in particular its statistical consistency, both in terms of the risk and the fair…
FAIREDU: A Multiple Regression-Based Method for Enhancing Fairness in Machine Learning Models for Educational Applications
Dainam University（大南大学）；VNU University of Engineering and Technology（越南国家大学工程技术大学）；Latrobe University（拉筹伯大学）；University of South Eastern Norway（东南挪威大学）
We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination with respect to sensitive attributes such as gender or ethnicity. This model is equivalent to a tractable convex optimization problem if a Wasserstein ball centered at the empirical distribution on the training data is used to model distributional uncertainty and if a new convex unfairness measure is used to incentivize equalized opportunities. We demonstrate that the resulting classifier improves fairness at a marginal loss of predictive accuracy on both synthetic and real da…
