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 language | English |
---|---|
Title of host publication | 35th aaai conference on artificial intelligence 33rd conference on innovative applications of artificial intelligence the eleventh symposium on educational advances in artificial intelligence |
Publisher | Association for the Advancement of Artificial Intelligence (AAAI) |
Pages | 8967-8974 |
ISBN (Electronic) | 978-1-57735-866-4 |
Publication status | Published - 2021 |
Event | 35th AAAI Conference on Artificial Intelligence - Online Duration: 2 Feb 2021 → 9 Feb 2021 Conference number: 35 |
Conference
Conference | 35th AAAI Conference on Artificial Intelligence |
---|---|
Abbreviated title | AAAI 2021 |
Period | 2/02/21 → 9/02/21 |
Keywords
- Calibration & Uncertainty Quantification
- Learning Theory