Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'

TL;DR

This paper compares MultiFIT, a multiscale independence test, with kernel-based HSIC tests, highlighting exact level control and discussing performance limitations in terms of test power.

Contribution

It provides a comparative analysis of MultiFIT and kernel tests, emphasizing exact level control and exploring their relative performance.

Findings

MultiFIT has exact level control at finite sample sizes.

Kernel tests based on HSIC also allow exact level control.

MultiFIT shows some limitations in test power in experiments.

Abstract

We discuss how MultiFIT, the Multiscale Fisher's Independence Test for Multivariate Dependence proposed by Gorsky and Ma (2022), compares to existing linear-time kernel tests based on the Hilbert-Schmidt independence criterion (HSIC). We highlight the fact that the levels of the kernel tests at any finite sample size can be controlled exactly, as it is the case with the level of MultiFIT. In our experiments, we observe some of the performance limitations of MultiFIT in terms of test power.