Unsupervised Adaptation for Fairness under Covariate Shift

Jatin Chauhan, Shreyas Havaldar, Karthikeyan Shanmugam, Jay Nandy, Aravindan Raghuveer

Keywords: Out of Distribution, Fairness, Unsupervised, Adaptation

TL;DR: We propose an unsupervised adaptation algorithm to address fairness under covariate shift. Our proposed objective involves the standard training loss along with a novel min-max entropy formulation to handle shift and a wasserstein loss for fairness.

Abstract: Training fair models typically involves optimizing a composite objective accounting for both prediction accuracy and some fairness measure. However, due to a shift in the distribution of the covariates at test time, the learnt fairness tradeoffs may no longer be valid, which we verify experimentally. To address this, we consider an unsupervised adaptation problem of training fair classifiers when only a small set of unlabeled test samples is available along with a large labeled training set. We propose a novel modification to the traditional composite objective by adding a weighted entropy objective on the unlabeled test dataset. This involves a min-max optimization where weights are optimized to mimic the importance weighting ratios followed by classifier optimization. We demonstrate that our weighted entropy objective provides an upper bound on the standard importance sampled training objective common in covariate shift formulations under some mild conditions. Experimentally, we demonstrate that Wasserstein distance based penalty for representation matching across protected sub groups together with the above loss outperforms existing baselines. Our method achieves the best accuracy-equalized odds tradeoff under the covariate shift setup. We find that, for the same accuracy, we get upto 2x improvement in equalized odds on notable benchmarks.

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