{"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-inference-a-review-for","title":"Variational Inference: A Review for Statisticians","arxiv_id":"1601.00670","date":"2016-01-04","proceeding":null,"authors":["David M. Blei","Alp Kucukelbir","Jon D. McAuliffe"],"abstract":"One of the core problems of modern statistics is to approximate\ndifficult-to-compute probability densities. This problem is especially\nimportant in Bayesian statistics, which frames all inference about unknown\nquantities as a calculation involving the posterior density. In this paper, we\nreview variational inference (VI), a method from machine learning that\napproximates probability densities through optimization. VI has been used in\nmany applications and tends to be faster than classical methods, such as Markov\nchain Monte Carlo sampling. The idea behind VI is to first posit a family of\ndensities and then to find the member of that family which is close to the\ntarget. Closeness is measured by Kullback-Leibler divergence. We review the\nideas behind mean-field variational inference, discuss the special case of VI\napplied to exponential family models, present a full example with a Bayesian\nmixture of Gaussians, and derive a variant that uses stochastic optimization to\nscale up to massive data. We discuss modern research in VI and highlight\nimportant open problems. VI is powerful, but it is not yet well understood. Our\nhope in writing this paper is to catalyze statistical research on this class of\nalgorithms.","url_abs":"http://arxiv.org/abs/1601.00670v9","url_pdf":"http://arxiv.org/pdf/1601.00670v9.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-inference-a-review-for","repo_url":"https://github.com/bdemeshev/om_ts","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"variational-inference-a-review-for","repo_url":"https://github.com/haziqj/ubd-bgtvi","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"variational-inference-a-review-for","repo_url":"https://github.com/magister-informatica-uach/INFO320","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Unlicense"}},{"paper_slug":"variational-inference-a-review-for","repo_url":"https://github.com/magister-informatica-uach/INFO3XX","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Unlicense"}},{"paper_slug":"variational-inference-a-review-for","repo_url":"https://github.com/taohu88/BayesianML","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"variational-inference-a-review-for","repo_url":"https://github.com/taolicheng/Deep-Learning-Learning-Path","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1601.00670","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}