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(2022) IEEE CONTROL SYSTEMS LETTERS 2475-1456 6 860-865

Exact Distribution-Free Hypothesis Tests for the Regression Function of Binary Classification via Conditional Kernel Mean Embeddings

doi.org/10.1109/LCSYS.2021.3087409
Széchenyi Plusz RRF
Abstract

In this letter we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines both the Bayes optimal classifier and the misclassification probabilities. A resampling based framework is presented and combined with consistent point estimators of the conditional kernel mean map, in order to construct distribution-free hypothesis tests. These tests are introduced in a flexible manner allowing us to control the exact probability of type I error for any sample size. We also prove that both proposed techniques are consistent under weak statistical assumptions, i.e., the type II error probabilities pointwise converge to zero.

Authors
Ambrus Tamás
Balázs Csanád Csáji
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