196,169 research outputs found
General Fair Empirical Risk Minimization
No full textWe 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 of [1] 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 Genoa1, 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
Pac-Bayes and fairness: Risk and fairness bounds on distribution dependent fair priors
No full textWe address the problem of algorithmic fairness: ensuring that sensitive information does not unfairly influence the outcome of a classifier. We face this issue in the PAC-Bayes framework and we present an approach which trades off and bounds the risk and the fairness of the Gibbs Classifier measured with respect to different state-of-the-art fairness measures. For this purpose, we further develop the idea that the PAC-Bayes prior can be defined based on the data-generating distribution without actually needing to know it. In particular, we define a prior and a posterior which gives more weight to functions which exhibit good generalization and fairness properties
Meta-learning with stochastic linear bandits
No full textWe investigate meta-learning procedures in the setting of stochastic linear bandits tasks. The goal is to select a learning algorithm which works well on average over a class of bandits tasks, that are sampled from a task-distribution. Inspired by recent work on learning-to-learn linear regression, we consider a class of bandit algorithms that implement a regularized version of the wellknown OFUL algorithm, where the regularization is a square euclidean distance to a bias vector. We first study the benefit of the biased OFUL algorithm in terms of regret minimization. We then propose two strategies to estimate the bias within the learning-to-learn setting. We show both theoretically and experimentally, that when the number of tasks grows and the variance of the task-distribution is small, our strategies have a significant advantage over learning the tasks in isolation
Entropy conditions for L r -convergence of empirical processes
No full textThe law of large numbers (LLN) over classes of functions is a classical topic of empirical processes theory. The properties characterizing classes of functions on which the LLN holds uniformly (i.e. Glivenko–Cantelli classes) have been widely studied in the literature. An elegant suffi cient condition for such a property is finiteness of the Koltchinskii–Pollard entropy integral, and other conditions have been formulated in terms of suitable combinatorial complexities (e.g. the Vapnik– Chervonenkis dimension). In this paper, we endow the class of functions F with a probability measure and consider the LLN relative to the associated Lr metric. This framework extends the case of uniform convergence over F , which is recovered when r goes to infinity. The main result is a Lr -LLN in terms of a suitable uniform entropy integral which generalizes the Koltchinskii–Pollard entropy integra
Randomized learning and generalization of fair and private classifiers: From PAC-Bayes to stability and differential privacy
No full textWe address the problem of randomized learning and generalization of fair and private classifiers. From one side we want to ensure that sensitive information does not unfairly influence the outcome of a classifier. From the other side we have to learn from data while preserving the privacy of individual observations. We initially face this issue in the PAC-Bayes framework presenting an approach which trades off and bounds the risk and the fairness of the randomized (Gibbs) classifier. Our new approach is able to handle several different state-of-the-art fairness measures. For this purpose, we further develop the idea that the PAC-Bayes prior can be defined based on the data-generating distribution without actually knowing it. In particular, we define a prior and a posterior which give more weight to functions with good generalization and fairness properties. Furthermore, we will show that this randomized classifier possesses interesting stability properties using the algorithmic distribution stability theory. Finally, we will show that the new posterior can be exploited to define a randomized accurate and fair algorithm. Differential privacy theory will allow us to derive that the latter algorithm has interesting privacy preserving properties ensuring our threefold goal of good generalization, fairness, and privacy of the final model
Learning fair and transferable representations with theoretical guarantees
No full textDeveloping learning methods which do not discriminate subgroups in the population is the central goal of algorithmic fairness. One way to reach this goal is by modifying the data representation in order to satisfy prescribed fairness constraints. This allows to reuse the same representation in other context (tasks) without discriminate subgroups. In this work we measure fairness according to demographic parity, requiring the probability of the possible model decisions to be independent of the sensitive information. We argue that the goal of imposing demographic parity can be substantially facilitated within a multi-task learning setting. We leverage task similarities by encouraging a shared fair representation across the tasks via low rank matrix factorization. We derive learning bounds establishing that the learned representation transfers well to novel tasks both in terms of prediction performance and fairness metrics. We present experiments on three real world datasets, showing that the proposed method outperforms state-of-the-art approaches by a significant margin
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