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 analyze 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.

翻译：本文研究标签偏移量化问题。我们提出了标签分布的鲁棒估计器，该估计器被证明与最大似然估计器相吻合。我们分析了理论层面，推导了所提方法的偏差界限，在正确设定情况下提供最优保证，同时对异常值和污染具有显著的鲁棒性。我们的结果为最大似然标签偏移鲁棒性的实证观察提供了理论验证。