Feature Noise Induces Loss Discrepancy Across Groups

TL;DR

This paper demonstrates that feature noise can cause loss discrepancy across groups even without information deficiency, affecting model fairness and performance depending on group distribution differences.

Contribution

It reveals feature noise as a subtle cause of loss discrepancy, providing theoretical analysis and empirical validation across datasets.

Findings

Feature noise induces loss discrepancy even with infinite data.

Loss discrepancy persists under distribution shifts that align group moments.

Feature noise impacts groups differently based on their distribution differences.

Abstract

The performance of standard learning procedures has been observed to differ widely across groups. Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). In this work, we point to a more subtle source of loss discrepancy---feature noise. Our main result is that even when there is no information deficiency specific to one group (e.g., both groups have infinite data), adding the same amount of feature noise to all individuals leads to loss discrepancy. For linear regression, we thoroughly characterize the effect of feature noise on loss discrepancy in terms of the amount of noise, the difference between moments of the two groups, and whether group information is used or not. We then show this loss discrepancy does not vanish immediately if a shift in distribution causes the groups to have similar moments. On three real-world datasets, we show feature noise increases the loss discrepancy if groups have different distributions, while it does not affect the loss discrepancy on datasets where groups have similar distributions.