Consistency and Finite Sample Behavior of Binary Class Probability Estimation


  • Alexander Mey Delft University of Technology
  • Marco Loog Delft University of Technology University of Copenhagen


Calibration & Uncertainty Quantification, Learning Theory


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.




How to Cite

Mey, A., & Loog, M. (2021). Consistency and Finite Sample Behavior of Binary Class Probability Estimation. Proceedings of the AAAI Conference on Artificial Intelligence, 35(10), 8967-8974. Retrieved from



AAAI Technical Track on Machine Learning III