On the Direction of Discrimination: An Information-Theoretic Analysis of Disparate Impact in Machine Learning
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In the context of machine learning, disparate impact refers to a form of systematic discrimination whereby the output distribution of a model depends on the value of a sensitive attribute (e.g., race or gender). In this paper, we present an information-theoretic framework to analyze the disparate impact of a binary classification model. We view the model as a fixed channel, and quantify disparate impact as the divergence in output distributions over two groups. We then aim to find a correction function that can be used to perturb the input distributions of each group in order to align their output distributions. We present an optimization problem that can be solved to obtain a correction function that will make the output distributions statistically indistinguishable. We derive closed-form expression for the correction function that can be used to compute it efficiently. We illustrate the use of the correction function for a recidivism prediction application derived from the ProPublica COMPAS dataset.
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