A Unified View of Label Shift Estimation

• URL: http://arxiv.org/abs/2003.07554v3
• Date: Fri, 16 Oct 2020 19:23:32 GMT
• Title: A Unified View of Label Shift Estimation
• Authors: Saurabh Garg, Yifan Wu, Sivaraman Balakrishnan, Zachary C. Lipton
• Abstract summary: There are two dominant approaches for estimating the label marginal. We present a unified view of the two methods and the first theoretical characterization of MLLS. Our analysis attributes BBSE's statistical inefficiency to a loss of information due to coarse calibration.
• Score: 45.472049320861856
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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