As algorithms increasingly inform and influence decisions made about individuals, it becomes increasingly important to address concerns that these algorithms might be discriminatory. The output of an algorithm can be discriminatory for many reasons, most notably: (1) the data used to train the algorithm might be biased (in various ways) to favor certain populations over others; (2) the analysis of this training data might inadvertently or maliciously introduce biases that are not borne out in the data. This work focuses on the latter concern. We develop and study multicalbration -- a new measure of algorithmic fairness that aims to mitigate concerns about discrimination that is introduced in the process of learning a predictor from data. Multicalibration guarantees accurate (calibrated) predictions for every subpopulation that can be identified within a specified class of computations. We think of the class as being quite rich; in particular, it can contain many overlapping subgroups of a protected group. We show that in many settings this strong notion of protection from discrimination is both attainable and aligned with the goal of obtaining accurate predictions. Along the way, we present new algorithms for learning a multicalibrated predictor, study the computational complexity of this task, and draw new connections to computational learning models such as agnostic learning.
On a technical level, both works draw connections between agnostic learning and the task of finding a group on which the fairness condition is violated ( @cite_12 refer to this as auditing). Leveraging this connection, we show how to use an agnostic learner to learn a multicalibrated predictor efficiently. In a similar vein, @cite_12 show how to use an agnostic learner to efficiently learn a classifier that satisfies balance or parity on a collection of sets, while achieving competitive accuracy within a given class. They also implement a more-practical variant of their algorithm and use it to conduct empirical experiments.
@cite_12
2768894107 2097373287 2117756453 2067831363
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. We study agnostic active learning, where the goal is to learn a classifier in a pre-specified hypothesis class interactively with as few label queries as possible, while making no assumptions on the true function generating the labels. The main algorithms for this problem are disagreement-based active learning , which has a high label requirement, and margin-based active learning , which only applies to fairly restricted settings. A major challenge is to find an algorithm which achieves better label complexity, is consistent in an agnostic setting, and applies to general classification problems. In this paper, we provide such an algorithm. Our solution is based on two novel contributions -- a reduction from consistent active learning to confidence-rated prediction with guaranteed error, and a novel confidence-rated predictor. We present an agnostic active learning algorithm for any hypothesis class of bounded VC dimension under arbitrary data distributions. Most previous work on active learning either makes strong distributional assumptions, or else is computationally prohibitive. Our algorithm extends the simple scheme of Cohn, Atlas, and Ladner [1] to the agnostic setting, using reductions to supervised learning that harness generalization bounds in a simple but subtle manner. We provide a fall-back guarantee that bounds the algorithm's label complexity by the agnostic PAC sample complexity. Our analysis yields asymptotic label complexity improvements for certain hypothesis classes and distributions. We also demonstrate improvements experimentally. We consider efficient agnostic learning of linear combinations of basis functions when the sum of absolute values of the weights of the linear combinations is bounded. With the quadratic loss function, we show that the class of linear combinations of a set of basis functions is efficiently agnostically learnable if and only if the class of basis functions is efficiently agnostically learnable. We also show that the sample complexity for learning the linear combinations grows polynomially if and only if a combinatorial property of the class of basis functions, called the fat-shattering function, grows at most polynomially. We also relate the problem to agnostic learning of f0 1g-valued function classes by showing that if a class of f0 1g-valued functions is efficiently agnostically learnable (using the same function class) with the discrete loss function, then the class of linear combinations of functions from the class is efficiently agnostically learnable with the quadratic loss function.