We study the problem of fair classification within the versatile framework of [ITCS 2012], which assumes the existence of a metric that measures similarity between pairs of individuals. Unlike previous works on metric-based fairness, we do not assume that the entire metric is known to the learning algorithm. Instead, we study the setting where a learning algorithm can query this metric a bounded number of times to ascertain similarities between particular pairs of individuals. For example, the queries might be answered by a panel of specialists spanning social scientists, statisticians, demographers, and ethicists. We propose "metric multifairness," a new definition of fairness that is parameterized by a similarity metric @math on pairs of individuals and a collection @math of"comparison sets" over pairs of individuals. One way to view this collection is as the family of comparisons that can be expressed within some computational bound. With this interpretation, metric multifairnesss loosely guarantees that similar subpopulations are treated similarly, as long as these subpopulations can be identified within this bound. In particular, metric multifairness implies that a rich class of subpopulations are protected from a multitude of discriminatory behaviors. We provide a general-purpose framework for learning a metric multifair hypothesis that achieves near-optimal loss from a small number of random samples from the metric @math . We study the sample complexity and time complexity of learning a metric multifair hypothesis (providing rather tight upper and lower bounds) by connecting it to the task of learning the class @math . In particular, if the class @math admits an efficient agnostic learner, then we can learn such a metric multifair hypothesis efficiently.
Finally, two recent theoretical works also investigate extensions to the fairness through awareness framework of @cite_11 . Gillen @cite_4 study metric-based individually fair online decision-making in the presence of an unknown fairness metric. In their setting, every day, a decision maker must choose between candidates available on that day; the goal is to have the decision maker's choices appear metric fair on each day (but not across days). Their work makes a strong learnability assumption about the underlying metric; in particular, they assume that the unknown metric is a Mahalanobis metric, whereas our focus is on fair classification when the metric is unknown and unrestricted. Rothblum and Yona @cite_5 study fair machine learning under a different relaxation of metric fairness, which they call approximate metric fairness. They assume that the metric is fully specified and known to the learning algorithm, whereas our focus is on addressing the challenge of an unknown metric. Their notion of approximate metric fairness aims to protect all (large enough) groups, and thus, is more strict than metric multifairness.
@cite_5 @cite_4 @cite_11
2788842311 2142863987 2949579938 2912501354
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. Metric learning aims at finding a distance that approximates a task-specific notion of semantic similarity. Typically, a Mahalanobis distance is learned from pairs of data labeled as being semantically similar or not. In this paper, we learn such metrics in a weakly supervised setting where "bags" of instances are labeled with "bags" of labels. We formulate the problem as a multiple instance learning (MIL) problem over pairs of bags. If two bags share at least one label, we label the pair positive, and negative otherwise. We propose to learn a metric using those labeled pairs of bags, leading to MildML, for multiple instance logistic discriminant metric learning. MildML iterates between updates of the metric and selection of putative positive pairs of examples from positive pairs of bags. To evaluate our approach, we introduce a large and challenging data set, Labeled Yahoo! News, which we have manually annotated and contains 31147 detected faces of 5873 different people in 20071 images. We group the faces detected in an image into a bag, and group the names detected in the caption into a corresponding set of labels. When the labels come from manual annotation, we find that MildML using the bag-level annotation performs as well as fully supervised metric learning using instance-level annotation. We also consider performance in the case of automatically extracted labels for the bags, where some of the bag labels do not correspond to any example in the bag. In this case MildML works substantially better than relying on noisy instance-level annotations derived from the bag-level annotation by resolving face-name associations in images with their captions. We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive formulations for global, multi-task and local metric learning. The resulting algorithms have several advantages over existing methods in the literature: a much smaller number of parameters to be estimated and a principled way to generalize learned metrics to new testing data points. To analyze the approach theoretically, we derive a generalization bound that justifies the sparse combination. Empirically, we evaluate our algorithms on several datasets against state-of-the-art metric learning methods. The results are consistent with our theoretical findings and demonstrate the superiority of our approach in terms of classification performance and scalability. 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 fairness measure. We then specialize our approach to kernel methods and propose a convex fair estimator in that setting. We test the estimator on a commonly used benchmark dataset (Communities and Crime) and on a new dataset collected at the University of Genova, containing the information of the academic career of five thousand students. The latter dataset provides a challenging real case scenario of unfair behaviour of standard regression methods that benefits from our methodology. The experimental results show that our estimator is effective at mitigating the trade-off between accuracy and fairness requirements.