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.

翻译：我们讨论了Gorsky和Ma(2022年)提议的多层渔业独立测试(多层渔业独立测试)与基于Hilbert-Schmidt独立标准的现有线性内核测试(HSIC)的对比情况。我们强调,任何有限样本大小的内核测试水平都可以完全控制,正如多层渔业独立测试一样。在我们的实验中,我们观察到了多层渔业独立测试在测试能力方面的一些性能限制。