Remarks on kernel Bayes' rule

TL;DR

This paper critically examines kernel Bayes' rule, revealing its limitations and unnatural predictions in certain cases due to assumption violations, through theoretical analysis and experiments.

Contribution

The paper provides a theoretical and experimental critique of kernel Bayes' rule, highlighting its limitations and the conditions under which it fails.

Findings

Kernel Bayes' rule can produce unnatural predictions.

Assumptions in kernel Bayes' rule often do not hold in practice.

Theoretical and experimental evidence shows limitations of the method.

Abstract

Kernel Bayes' rule has been proposed as a nonparametric kernel-based method to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we demonstrate both theoretically and experimentally that the prediction result by kernel Bayes' rule is in some cases unnatural. We consider that this phenomenon is in part due to the fact that the assumptions in kernel Bayes' rule do not hold in general.