In recent years, significant work has been done to include fairness constraints in the training objective of machine learning algorithms. Many state-of the-art algorithms tackle this challenge by learning a fair representation which captures all the relevant information to predict the output Y while not containing any information about a sensitive attribute S. In this paper, we propose an adversarial algorithm to learn unbiased representations via the Hirschfeld-Gebelein-Renyi (HGR) maximal correlation coefficient. We leverage recent work which has been done to estimate this coefficient by learning deep neural network transformations and use it as a minmax game to penalize the intrinsic bias in a multi dimensional latent representation. Compared to other dependence measures, the HGR coefficient captures more information about the non-linear dependencies with the sensitive variable, making the algorithm more efficient in mitigating bias in the representation. We empirically evaluate and compare our approach and demonstrate significant improvements over existing works in the field.

The past few years have seen a dramatic rise of academic and societal interest in fair machine learning. While plenty of fair algorithms have been proposed recently to tackle this challenge for discrete variables, only a few ideas exist for continuous ones. The objective in this paper is to ensure some independence level between the outputs of regression models and any given continuous sensitive variables. For this purpose, we use the Hirschfeld-Gebelein-R enyi (HGR) maximal correlation coefficient as a fairness metric. We propose two approaches to minimize the HGR coefficient. First, by reducing an upper bound of the HGR with a neural network estimation of the χ 2 divergence. The idea is to predict the output Y while minimizing the ability of an adversarial neural network to find the estimated transformations which are required to predict the HGR coefficient. We empirically assess and compare our approaches and demonstrate significant improvements on previously presented work in the field. 1 Introduction The use of machine learning algorithms in our day-to-day life has become ubiquitous. However, when trained on biased data, those algorithms are prone to learn, perpetuate or even reinforce these biases [6]. Because many applications have far-reaching consequences (credit rating, insurance pricing, recidivism score, etc.), there is an increasing concern in society that the use of machine learning models could reproduce discrimination based on sensitive attributes such as gender, race, age, weight, or other.