Maximum Likelihood with Bias-Corrected Calibration is Hard-To-Beat at Label Shift Adaptation

TL;DR

This paper demonstrates that maximum likelihood combined with bias-corrected calibration effectively addresses label shift in distribution, outperforming state-of-the-art methods without requiring model retraining.

Contribution

It shows that combining maximum likelihood with bias-corrected calibration surpasses existing methods like BBSL and RLLS in label shift adaptation, and provides theoretical and practical insights.

Findings

Maximum likelihood with bias-corrected calibration outperforms BBSL and RLLS.

The maximum likelihood objective is proven to be concave.

A new strategy for estimating source priors enhances robustness.

Abstract

Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to scenarios where the baseline prevalence of the disease is different. Given estimates of p(y|x) from a predictive model, Saerens et al. proposed an efficient maximum likelihood algorithm to correct for label shift that does not require model retraining, but a limiting assumption of this algorithm is that p(y|x) is calibrated, which is not true of modern neural networks. Recently, Black Box Shift Learning (BBSL) and Regularized Learning under Label Shifts (RLLS) have emerged as state-of-the-art techniques to cope with label shift when a classifier does not output calibrated probabilities, but both methods require model retraining with importance weights and neither has been benchmarked against maximum likelihood. Here we (1) show that combining maximum likelihood with a type of calibration we call bias-corrected calibration outperforms both BBSL and RLLS across diverse datasets and distribution shifts, (2) prove that the maximum likelihood objective is concave, and (3) introduce a principled strategy for estimating source-domain priors that improves robustness to poor calibration. This work demonstrates that the maximum likelihood with appropriate calibration is a formidable and efficient baseline for label shift adaptation; notebooks reproducing experiments available at https://github.com/kundajelab/labelshiftexperiments