Hunting for Discriminatory Proxies in Linear Regression Models

A machine learning model may exhibit discrimination when used to make decisions involving people. One potential cause for such outcomes is that the model uses a statistical proxy for a protected demographic attribute. In this paper we formulate a definition of proxy use for the setting of linear regression and present algorithms for detecting proxies. Our definition follows recent work on proxies in classification models, and characterizes a model's constituent behavior that: 1) correlates closely with a protected random variable, and 2) is causally influential in the overall behavior of the model. We show that proxies in linear regression models can be efficiently identified by solving a second-order cone program, and further extend this result to account for situations where the use of a certain input variable is justified as a business necessity''.