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A Kernel Test of Goodness of Fit

Chwialkowski, K; Strathmann, H; Gretton, A; (2016) A Kernel Test of Goodness of Fit. In: ICML ’16: Proceedings of the 32nd International Conference on Machine Learning. (pp. pp. 2606-2615). JMLR: Workshop and Conference Proceedings Green open access

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Abstract

We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence constructed via Stein's method using functions from a Reproducing Kernel Hilbert Space. Our test statistic is based on an empirical estimate of this divergence, taking the form of a V-statistic in terms of the log gradients of the target density and the kernel. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, where we estimate the null distribution quantiles using a wild bootstrap procedure. We apply our test to quantifying convergence of approximate Markov Chain Monte Carlo methods, statistical model criticism, and evaluating quality of fit vs model complexity in nonparametric density estimation.

Type: Proceedings paper
Title: A Kernel Test of Goodness of Fit
Event: International Conference on Machine Learning
Open access status: An open access version is available from UCL Discovery
Publisher version: http://proceedings.mlr.press/v48/chwialkowski16.pd...
Language: English
Additional information: Copyright 2016 by the author(s)
Keywords: stat.ML, stat.ML
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: http://discovery.ucl.ac.uk/id/eprint/1496379
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