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

03/08/2021

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by   Ambrus Tamás, et al.

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In this paper 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 applied and combined with consistent point estimators for the conditional kernel mean map 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. We also prove that both proposed techniques are consistent under weak statistical assumptions, i.e., the type II error probabilities pointwise converge to zero.