{"id":556434,"date":"2018-12-09T20:09:43","date_gmt":"2018-12-10T04:09:43","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=556434"},"modified":"2018-12-09T20:10:20","modified_gmt":"2018-12-10T04:10:20","slug":"random-feature-stein-discrepancies","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/random-feature-stein-discrepancies\/","title":{"rendered":"Random Feature Stein Discrepancies"},"content":{"rendered":"<div id=\"rfsd\" class=\"in\">\n<p>Computable Stein discrepancies have been deployed for a variety of applications, including sampler selection in posterior inference, approximate Bayesian inference, and goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they exhibit avoidable degradations in testing power&#8212;even when power is explicitly optimized. To address these shortcomings, we introduce feature Stein discrepancies (\u03a6SDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct \u03a6SDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations&#8212;random \u03a6SDs (R\u03a6SDs)&#8212;which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, R\u03a6SDs typically perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Computable Stein discrepancies have been deployed for a variety of applications, including sampler selection in posterior inference, approximate Bayesian inference, and goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they 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