{"id":5704,"date":"2025-07-30T07:03:54","date_gmt":"2025-07-30T07:03:54","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/07\/30\/2507-21434\/"},"modified":"2025-07-30T07:03:54","modified_gmt":"2025-07-30T07:03:54","slug":"2507-21434","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/07\/30\/2507-21434\/","title":{"rendered":"Measuring Sample Quality with Copula Discrepancies"},"content":{"rendered":"

Measuring Sample Quality with Copula Discrepancies
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arXiv:2507.21434v1 Announce Type: new
\nAbstract: The scalable Markov chain Monte Carlo (MCMC) algorithms that underpin modern Bayesian machine learning, such as Stochastic Gradient Langevin Dynamics (SGLD), sacrifice asymptotic exactness for computational speed, creating a critical diagnostic gap: traditional sample quality measures fail catastrophically when applied to biased samplers. While powerful Stein-based diagnostics can detect distributional mismatches, they provide no direct assessment of dependence structure, often the primary inferential target in multivariate problems. We introduce the Copula Discrepancy (CD), a principled and computationally efficient diagnostic that leverages Sklar’s theorem to isolate and quantify the fidelity of a sample’s dependence structure independent of its marginals. Our theoretical framework provides the first structure-aware diagnostic specifically designed for the era of approximate inference. Empirically, we demonstrate that a moment-based CD dramatically outperforms standard diagnostics like effective sample size for hyperparameter selection in biased MCMC, correctly identifying optimal configurations where traditional methods fail. Furthermore, our robust MLE-based variant can detect subtle but critical mismatches in tail dependence that remain invisible to rank correlation-based approaches, distinguishing between samples with identical Kendall’s tau but fundamentally different extreme-event behavior. With computational overhead orders of magnitude lower than existing Stein discrepancies, the CD provides both immediate practical value for MCMC practitioners and a theoretical foundation for the next generation of structure-aware sample quality assessment.<\/div>\n

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\n Agnideep Aich, Ashit Baran Aich, Bruce Wade
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Measuring Sample Quality with Copula Discrepancies arXiv:2507.21434v1 Announce Type: new Abstract: The scalable Markov chain Monte Carlo (MCMC) algorithms that underpin modern Bayesian machine learning, such as Stochastic Gradient Langevin Dynamics (SGLD), sacrifice asymptotic exactness for computational speed, creating a critical diagnostic gap: traditional sample quality measures fail catastrophically when applied to biased samplers. While […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[189,618,31],"class_list":["post-5704","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-based","tag-quality","tag-sample"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5704"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=5704"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5704\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5704"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5704"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5704"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}