# Two-sample Statistics Based on Anisotropic Kernels

14 Sep 2017  ·  , , ·

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorporating local covariance matrices and constructing an anisotropic kernel. The kernel matrix is asymmetric; it computes the affinity between $n$ data points and a set of $n_R$ reference points, where $n_R$ can be drastically smaller than $n$. While the proposed statistic can be viewed as a special class of Reproducing Kernel Hilbert Space MMD, the consistency of the test is proved, under mild assumptions of the kernel, as long as $\|p-q\| \sqrt{n} \to \infty$, and a finite-sample lower bound of the testing power is obtained. Applications to flow cytometry and diffusion MRI datasets are demonstrated, which motivate the proposed approach to compare distributions.

PDF Abstract

## Datasets

Add Datasets introduced or used in this paper

## Results from the Paper Edit

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

## Methods Add Remove

No methods listed for this paper. Add relevant methods here