{"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/variational-bayesian-monte-carlo","title":"Variational Bayesian Monte Carlo","arxiv_id":"1810.05558","date":"2018-10-12","proceeding":"NeurIPS 2018 12","authors":["Luigi Acerbi"],"abstract":"Many probabilistic models of interest in scientific computing and machine\nlearning have expensive, black-box likelihoods that prevent the application of\nstandard techniques for Bayesian inference, such as MCMC, which would require\naccess to the gradient or a large number of likelihood evaluations. We\nintroduce here a novel sample-efficient inference framework, Variational\nBayesian Monte Carlo (VBMC). VBMC combines variational inference with\nGaussian-process based, active-sampling Bayesian quadrature, using the latter\nto efficiently approximate the intractable integral in the variational\nobjective. Our method produces both a nonparametric approximation of the\nposterior distribution and an approximate lower bound of the model evidence,\nuseful for model selection. We demonstrate VBMC both on several synthetic\nlikelihoods and on a neuronal model with data from real neurons. Across all\ntested problems and dimensions (up to $D = 10$), VBMC performs consistently\nwell in reconstructing the posterior and the model evidence with a limited\nbudget of likelihood evaluations, unlike other methods that work only in very\nlow dimensions. Our framework shows great promise as a novel tool for posterior\nand model inference with expensive, black-box likelihoods.","url_abs":"http://arxiv.org/abs/1810.05558v2","url_pdf":"http://arxiv.org/pdf/1810.05558v2.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":"variational-bayesian-monte-carlo","repo_url":"https://github.com/lacerbi/infbench","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"variational-bayesian-monte-carlo","repo_url":"https://github.com/lacerbi/vbmc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"variational-bayesian-monte-carlo","repo_url":"https://github.com/acerbilab/pyvbmc","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"variational-bayesian-monte-carlo","repo_url":"https://github.com/rseny42/Variational-Bayesian-Monte-Carlo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1810.05558","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1810.05558"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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