Nonparametric statistical tests using kernels

Arthur Gretton (UCL)
Wednesday, July 6, 2016 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

I will describe a kernel approach to hypothesis testing, based on a representation of probability distributions in a reproducing kernel Hilbert space. I will first derive a metric as the distance between these representations. Next, I will describe both tests of homogeneity (of whether two samples are from the same distribution), and of independence (of whether a joint distribution factorises into a product of marginals). More recent work will follow, including statistical tests for random processes (for instance, to compare marginal distributions of Markov chains), tests for multi-variable interaction, and a test of goodness-of-fit based on Stein's method. This last test can be used even if the reference distribution is known only up to a normalising constant, making it suited to benchmarking MCMC and to statistical model criticism.