# Bounding the Error From Reference Set Kernel Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/1812.04594 · HTML: https://mlsanity.com/paper/1812.04594/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Kernel distance measures for time series, random fields and other structured data](https://mlsanity.com/paper/2109.14752/) (2021)

## Abstract (arXiv)

In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is quantified in terms of the speed in which heat diffuses from those points to the rest of the data, as well as how at the weights on the reference points are, and gives a non-asymptotic, non-probabilistic bound. The result ties into the problem of the eigenvector triple product, which appears in a number of important problems. The error bound also suggests an optimization scheme for choosing the best set of reference points and weights. The method is tested on a several two sample test examples.