Non-asymptotic analysis of label shift quantification: robustness and calibration

Abstract

In this paper, we investigate the label shift quantification problem. We propose robust estimators of the label distribution which turn out to coincide with the Maximum Likelihood Estimator. We analyse the theoretical aspects and derive deviation bounds for the proposed method, providing optimal guarantees in the well-specified case, along with notable robustness properties against outliers and contamination. Our results provide theoretical validation for empirical observations on the robustness of Maximum Likelihood Label Shift.