Empirical Bayes fairness in linear regression

Abstract

Bias in data may lead to prediction procedures which discriminate individuals from sensitive groups. In this paper we propose a Bayesian method for parameter estimation in the linear regression model taking fairness into ac- count. For a given prior structure, namely, the Normal-Gamma prior, for a specific choice of unfairness measure (which does not require the use of private -sensitive- information), our method computes a constrained empirical Bayes estimator that induces fairness in posterior predictions. Specifically, the model hyper-parameters are calculated as the optimal solution of a constrained optimization problem: that in which the marginal likelihood is maximized in a region where the unfairness measure is upper bounded and thus, controlled. This guarantees that average posterior predictions are, at most, as unfair as the upper bound establishes. Experi- ments with synthetic and real data sets show the competitiveness of our approach in terms of fairness in the obtained solution and prediction error.