This document provides additional examples and results for the authors' paper "Robust Permutation Tests For Correlation And Regression Coefficients".

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Many interesting problems in the Internet industry can be framed as a two-sided marketplace problem. Examples include search applications and recommender systems showing people, jobs, movies, products, restaurants, etc. Incorporating fairness while building such systems is crucial and can have deep social and economic impact (applications include job recommendations, recruiters searching for candidates, etc.). In this paper, we propose a definition and develop an end-to-end framework for achieving fairness while building such machine learning systems at scale. We extend prior work [29] to develop an optimization framework that can tackle fairness constraints from both the source and destination sides of the marketplace, as well as dynamic aspects of the problem. The framework is flexible enough to adapt to different definitions of fairness and can be implemented in very large-scale settings. We perform simulations to show the efficacy of our approach.Preprint. Under review.

Machine learning models are central to people's lives and impact society in ways as fundamental as determining how people access information. The gravity of these models imparts a responsibility to model developers to ensure that they are treating users in a fair and equitable manner. Before deploying a model into production, it is crucial to examine the extent to which its predictions demonstrate biases. This paper deals with the detection of bias exhibited by a machine learning model through statistical hypothesis testing. We propose a permutation testing methodology that performs a hypothesis test that a model is fair across two groups with respect to any given metric. There are increasingly many notions of fairness that can speak to different aspects of model fairness. Our aim is to provide a flexible framework that empowers practitioners to identify significant biases in any metric they wish to study. We provide a formal testing mechanism as well as extensive experiments to show how this method works in practice.

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