Controlling Attribute Effect in Linear Regression

Abstract

Abstract-In data mining we often have to learn from biased data, because, for instance, data comes from different batches or there was a gender or racial bias in the collection of social data. In some applications it may be necessary to explicitly control this bias in the models we learn from the data. This paper is the first to study learning linear regression models under constraints that control the biasing effect of a given attribute such as gender or batch number. We show how propensity modeling can be used for factoring out the part of the bias that can be justified by externally provided explanatory attributes. Then we analytically derive linear models that minimize squared error while controlling the bias by imposing constraints on the mean outcome or residuals of the models. Experiments with discrimination-aware crime prediction and batch effect normalization tasks show that the proposed techniques are successful in controlling attribute effects in linear regression models.

Adaptive Sensitive Reweighting to Mitigate Bias in Fairness-aware Classification

“…For example, there may exist weaker feature correlations (e.g. through a chain of correlation of unobserved features, which may require external explanatory attributes to identify [4]) that cause bias against only a subset of the sensitive group. Furthermore, certain data could cause biases to only certain types of classifiers.…”

“…Convex functions, such as exp(β i p), are Lipschitz-continuous in bounded sets [22]. 4 ± represents either the positive or the negative sign and ∓ its opposite sign.…”

“…Approaches training under fairness constraints select a disparate impact or mistreatment metric and attempt to properly adjust the training rules, either via editing the rules themselves [4,44] (e.g. by inserting an appropriate regularization term towards fairness) or by introducing appropriate linear program constraints [6,11,18,39,[42][43][44] that reflect the desired optimization goals.…”

Convex Fairness Constrained Model Using Causal Effect Estimators

“…This is called the red lining effect [8]. Furthermore, as described in [7], the non-sensitive features that cause indirect discrimination sometimes include features which cause bias but can be justified. These features are called explanatory features and the bias caused by the explanatory features are called explanatory bias.…”

“…These features are called explanatory features and the bias caused by the explanatory features are called explanatory bias. We treat such explanatory bias as non-discriminatory by following the work of [7], though explanatory bias is included in indirect discrimination. Figure 1 shows the relationship between discrimination and explanatory bias.…”