{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/random-feature-stein-discrepancies","title":"Random Feature Stein Discrepancies","arxiv_id":"1806.07788","date":"2018-06-20","proceeding":"NeurIPS 2018 12","authors":["Jonathan H. Huggins","Lester Mackey"],"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.","url_abs":"https://arxiv.org/abs/1806.07788v5","url_pdf":"https://arxiv.org/pdf/1806.07788v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"random-feature-stein-discrepancies","repo_url":"https://bitbucket.org/jhhuggins/random-feature-stein-discrepancies","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1806.07788","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}