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

arXiv: https://arxiv.org/abs/2206.11142 · HTML: https://mlsanity.com/paper/2206.11142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives](https://mlsanity.com/paper/1909.03302/) (2019)
- [A Kernel Independence Test for Random Processes](https://mlsanity.com/paper/1402.4501/) (2014)
- [An Adaptive Test of Independence with Analytic Kernel Embeddings](https://mlsanity.com/paper/1610.04782/) (2016)
- [A simpler condition for consistency of a kernel independence test](https://mlsanity.com/paper/1501.06103/) (2015)
- [Multiscale Fisher's Independence Test for Multivariate Dependence](https://mlsanity.com/paper/1806.06777/) (2018)

## Abstract (arXiv)

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.