A Unified View of Label Shift Estimation
Abstract
Under label shift, the label distribution p(y) might change but the class-conditional distributions p(x|y) do not. There are two dominant approaches for estimating the label marginal. BBSE, a moment-matching approach based on confusion matrices, is provably consistent and provides interpretable error bounds. However, a maximum likelihood estimation approach, which we call MLLS, dominates empirically. In this paper, we present a unified view of the two methods and the first theoretical characterization of MLLS. Our contributions include (i) consistency conditions for MLLS, which include calibration of the classifier and a confusion matrix invertibility condition that BBSE also requires; (ii) a unified framework, casting BBSE as roughly equivalent to MLLS for a particular choice of calibration method; and (iii) a decomposition of MLLS's finite-sample error into terms reflecting miscalibration and estimation error. Our analysis attributes BBSE's statistical inefficiency to a loss of information due to coarse calibration. Experiments on synthetic data, MNIST, and CIFAR10 support our findings.
Cite
@article{arxiv.2003.07554,
title = {A Unified View of Label Shift Estimation},
author = {Saurabh Garg and Yifan Wu and Sivaraman Balakrishnan and Zachary C. Lipton},
journal= {arXiv preprint arXiv:2003.07554},
year = {2020}
}
Comments
Accepted at Neurips 2020