﻿ 統計数理研究所｜統計的機械学習研究センター



Time: March 31, 2015. 15:00-
Place：Seminar Room 5

Speaker: Arthur Gretton (University College London)

Title: A Wild Bootstrap for Degenerate Kernel Tests
The maximum mean discrepancy (MMD) is a metric on probability measures, defined as the distance between expected features of these measures in a reproducing kernel Hilbert space (RKHS). This metric can be used as the statistic of a nonparametric homogeneity test, where two distributions are compared, and the null hypothesis is that the distributions are equal. The null is rejected when the MMD distance between the samples is sufficiently large. When the two samples being compared are drawn from two stationary random processes, then a comparison can be made of the stationary distributions of these random processes. I will describe a wild bootstrap method for simulating the quantiles of the null hypothesis for the MMD when two stationary random processes are compared. The new approach is contrasted with a standard permutation approach for i.i.d. data, which is shown to fail badly, and to return excessive false positives. In experiments, the wild bootstrap gives strong performance on synthetic examples, on audio data, and in performance benchmarking for the Gibbs sampler. The wild bootstrap may be used in other kernel tests as well: time permitting, I will discuss its application to independence testing between time series. With Kacper Chwialkowski, Dino Sejdinovic