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Random Feature Stein Discrepancies
Machine Learning · Submitted 20 Jun 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. | background 0.63 | 0.06 | 0.03 | asserted 1.00 |
| s2 | 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. | background 0.50 | 0.05 | 0.03 | asserted 1.00 |
| s3 | 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. | contribution 1.00 | 0.83 | 0.20 | asserted 1.00 |
| s4 | 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. | contribution 0.92 | 0.96 | 0.47 | asserted 1.00 |
| s5 | 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. | result 1.00 | 0.96 | 0.64 | asserted 1.00 |
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Original abstract
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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Other sets of random features, not based on Fourier transforms, have recently been advocated for tasks such as goodness-of-fit testing and evaluating the quality of Monte Carlo output [ref] .
A Note on Simulation-Based Inference by Matching Random Features · Random Features in Machine Learning · 0.90
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