Random Feature Stein Discrepancies.

ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 31 (NIPS 2018)(2018)

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摘要
Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to 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-even when power is explicitly optimized To address these shortcomings, we introduce feature Stein discrepancies (Phi)SDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct (Phi)SDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations-random (Phi)SDs (R Phi SDs)-which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, R(Phi)SDs perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.
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关键词
computational cost,sample size,importance sampling,random feature stein discrepancies
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