Consistency and Finite Sample Behavior of Binary Class Probability Estimation

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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.
Original languageEnglish
Title of host publication35th aaai conference on artificial intelligence 33rd conference on innovative applications of artificial intelligence the eleventh symposium on educational advances in artificial intelligence
PublisherAssociation for the Advancement of Artificial Intelligence (AAAI)
Pages8967-8974
ISBN (Electronic)978-1-57735-866-4
Publication statusPublished - 2021
Event35th AAAI Conference on Artificial Intelligence - Online
Duration: 2 Feb 20219 Feb 2021
Conference number: 35

Conference

Conference35th AAAI Conference on Artificial Intelligence
Abbreviated titleAAAI 2021
Period2/02/219/02/21

Keywords

  • Calibration & Uncertainty Quantification
  • Learning Theory

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