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Paper · 1602.02964 · 2016

A Kernel Test of Goodness of Fit

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 9 functions out of this paper's own repositories and ran 4 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
karlnapf/kernel_goodness_of_fit canonical 4 of 9
FunctionStatusWhere it lives
grad_log_dens Ran karlnapf/kernel_goodness_of_fit/2dimNormal/2dimNormal.py
code served (permissive licence) · get_code("70fb339d83a7c1bb")
logg Ran karlnapf/kernel_goodness_of_fit/2dimNormal/2dimNormal.py
code served (permissive licence) · get_code("e4354ae81ee91ddc")
simulate Ran karlnapf/kernel_goodness_of_fit/stat_test/ar.py
code served (permissive licence) · get_code("1f7f79604d019ecc")
simulatepm Ran karlnapf/kernel_goodness_of_fit/stat_test/ar.py
code served (permissive licence) · get_code("592b744c9e05ee29")
SGLD Not yet run karlnapf/kernel_goodness_of_fit/sgld_test/bimodal_SGLD.py
code served (permissive licence) · get_code("26b5447d97de57ad")
approximate_MH_accept Not yet run karlnapf/kernel_goodness_of_fit/samplers/austerity.py
code served (permissive licence) · get_code("a1e3a4b16545a1c2")
austerity Not yet run karlnapf/kernel_goodness_of_fit/samplers/austerity.py
code served (permissive licence) · get_code("6b7168e28268b01c")
evSGLD Not yet run karlnapf/kernel_goodness_of_fit/sgld_test/bimodal_SGLD.py
code served (permissive licence) · get_code("a48418d972eb4746")
metropolis_hastings Not yet run karlnapf/kernel_goodness_of_fit/samplers/MetropolisHastings.py
code served (permissive licence) · get_code("e7070853af855d53")

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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.

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