Discussion of Multiscale Fisher's Independence Test for Multivariate Dependence

Abstract: The multiscale Fisher's independence test (MULTIFIT hereafter) proposed by Gorsky & Ma (2022) is a novel method to test independence between two random vectors. By its design, this test is particularly useful in detecting local dependence. Moreover, by adopting a resampling-free approach, it can easily accommodate massive sample sizes. Another benefit of the proposed method is its ability to interpret the nature of dependency. We congratulate the authors, Shai Gorksy and Li Ma, for their very interesting and elegant work. In this comment, we would like to discuss a general framework unifying the MULTIFIT and other tests and compare it with the binary expansion randomized ensemble test (BERET hereafter) proposed by Lee et al. (In press). We also would like to contribute our thoughts on potential extensions of the method.