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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". Finally, we present empirical results on two law enforcement datasets that exhibit varying degrees of racial disparity in prediction outcomes, demonstrating that proxies shed useful light on the causes of discriminatory behavior in models.

Emerging scholarship suggests that the EU legal concept of direct discrimination - where a person is given different treatment on grounds of a protected characteristic - may apply to various algorithmic decision-making contexts. This has important implications: unlike indirect discrimination, there is generally no 'objective justification' stage in the direct discrimination framework, which means that the deployment of directly discriminatory algorithms will usually be unlawful per se. In this paper, we focus on the most likely candidate for direct discrimination in the algorithmic context, termed inherent direct discrimination, where a proxy is inextricably linked to a protected characteristic. We draw on computer science literature to suggest that, in the algorithmic context, 'treatment on the grounds of' needs to be understood in terms of two steps: proxy capacity and proxy use. Only where both elements can be made out can direct discrimination be said to be `on grounds of' a protected characteristic. We analyse the legal conditions of our proposed proxy capacity and proxy use tests. Based on this analysis, we discuss technical approaches and metrics that could be developed or applied to identify inherent direct discrimination in algorithmic decision-making.

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''. Finally, we present empirical results on two law enforcement datasets that exhibit varying degrees of racial disparity in prediction outcomes, demonstrating that proxies shed useful light on the causes of discriminatory behavior in 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''. Finally, we present empirical results on two law enforcement datasets that exhibit varying degrees of racial disparity in prediction outcomes, demonstrating that proxies shed useful light on the causes of discriminatory behavior in 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". Finally, we present empirical results on two law enforcement datasets that exhibit varying degrees of racial disparity in prediction outcomes, demonstrating that proxies shed useful light on the causes of discriminatory behavior in models.