第23回統計的機械学習セミナー(2015年3月31日)
Time: March 31, 2015. 15:00-
Place:Seminar Room 5
Speaker:
Arthur Gretton (University College London)
Title:
A Wild Bootstrap for Degenerate Kernel Tests
Abstract:
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