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.

arXiv commentAccepted at Neurips 2020

References in corpus (4)

• On Calibration of Modern Neural Networks
• Evaluating model calibration in classification
• Mixture Proportion Estimation via Kernel Embedding of Distributions
• Regularized Learning for Domain Adaptation under Label Shifts

Cited by in corpus (8)

• Online Adaptation to Label Distribution Shift
• Aggregating From Multiple Target-Shifted Sources
• Mixture Proportion Estimation and PU Learning: A Modern Approach
• MLDemon: Deployment Monitoring for Machine Learning Systems
• Contrastive Attraction and Contrastive Repulsion for Representation Learning
• Active Learning under Label Shift
• Domain Adaptation in Highly Imbalanced and Overlapping Datasets
• Inference with generalizable classifier predictions