A Kernel Test of Goodness of Fit

Kacper Chwialkowski, Heiko Strathmann, Arthur Gretton
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2606-2615, 2016.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-chwialkowski16, title = {A Kernel Test of Goodness of Fit}, author = {Chwialkowski, Kacper and Strathmann, Heiko and Gretton, Arthur}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {2606--2615}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/chwialkowski16.pdf}, url = {https://proceedings.mlr.press/v48/chwialkowski16.html}, 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.} }
Endnote
%0 Conference Paper %T A Kernel Test of Goodness of Fit %A Kacper Chwialkowski %A Heiko Strathmann %A Arthur Gretton %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-chwialkowski16 %I PMLR %P 2606--2615 %U https://proceedings.mlr.press/v48/chwialkowski16.html %V 48 %X 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.
RIS
TY - CPAPER TI - A Kernel Test of Goodness of Fit AU - Kacper Chwialkowski AU - Heiko Strathmann AU - Arthur Gretton BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-chwialkowski16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 2606 EP - 2615 L1 - http://proceedings.mlr.press/v48/chwialkowski16.pdf UR - https://proceedings.mlr.press/v48/chwialkowski16.html AB - 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. ER -
APA
Chwialkowski, K., Strathmann, H. & Gretton, A.. (2016). A Kernel Test of Goodness of Fit. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:2606-2615 Available from https://proceedings.mlr.press/v48/chwialkowski16.html.

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