Consistency and Finite Sample Behavior of Binary Class Probability Estimation

Conference paper (2021)

Authors

A. Mey Interactive Intelligence - EEMCS
M. Loog Pattern Recognition and Bioinformatics - EEMCS
Research Group
Pattern Recognition and Bioinformatics (EEMCS) (TU Delft)
Copyright: © 2021 A. Mey, M. Loog
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Published Date

2021

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Intelligent Systems

Research Group

Pattern Recognition and Bioinformatics

Abstract

We investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. We extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Following previous literature on excess risk bounds and proper scoring rules, we derive a class probability estimator based on empirical risk minimization. We then derive conditions under which this estimator will converge with high probability to the true class probabilities with respect to the L1-norm. One of our core contributions is a novel way to derive finite sample L1-convergence rates of this estimator for different surrogate loss functions. We also study in detail which commonly used loss functions are suitable for this estimation problem and briefly address the setting of model-misspecification.