Remarks on kernel Bayes' rule
This work identifies limitations in a foundational method for kernel-based Bayesian inference, which is incremental as it critiques an existing approach.
The paper demonstrates that kernel Bayes' rule, a nonparametric kernel-based method for Bayesian inference, can produce unnatural predictions in some cases, attributing this to its assumptions not holding generally.
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.