Fast and Scalable Score-Based Kernel Calibration Tests

Pierre Glaser, David Widmann, Fredrik Lindsten, Arthur Gretton

Keywords: Calibration, Hypothesis Testing, Goodness-of-fit, Kernel Methods

TL;DR: We introduce a Fast and Scalable Score-Based Kernel Calibration Test.

Abstract: We introduce the Kernel Calibration Conditional Stein Discrepancy test (KCCSD test), a nonparametric, kernel-based test for assessing the calibration of probabilistic models with well-defined scores. In contrast to previous methods, our test avoids the need for possibly expensive expectation approximations while providing control over its type-I error. We achieve these improvements by using a new family of kernels for score-based probabilities that can be estimated without probability density samples, and by using a Conditional Goodness of Fit criterion for the KCCSD test's U-statistic. We demonstrate the properties of our test on various synthetic settings.