{"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/estimating-mixture-models-via-mixtures-of","title":"Estimating Mixture Models via Mixtures of Polynomials","arxiv_id":"1603.08482","date":"2016-03-28","proceeding":"NeurIPS 2015 12","authors":["Sida I. Wang","Arun Tejasvi Chaganty","Percy Liang"],"abstract":"Mixture modeling is a general technique for making any simple model more\nexpressive through weighted combination. This generality and simplicity in part\nexplains the success of the Expectation Maximization (EM) algorithm, in which\nupdates are easy to derive for a wide class of mixture models. However, the\nlikelihood of a mixture model is non-convex, so EM has no known global\nconvergence guarantees. Recently, method of moments approaches offer global\nguarantees for some mixture models, but they do not extend easily to the range\nof mixture models that exist. In this work, we present Polymom, an unifying\nframework based on method of moments in which estimation procedures are easily\nderivable, just as in EM. Polymom is applicable when the moments of a single\nmixture component are polynomials of the parameters. Our key observation is\nthat the moments of the mixture model are a mixture of these polynomials, which\nallows us to cast estimation as a Generalized Moment Problem. We solve its\nrelaxations using semidefinite optimization, and then extract parameters using\nideas from computer algebra. This framework allows us to draw insights and\napply tools from convex optimization, computer algebra and the theory of\nmoments to study problems in statistical estimation.","url_abs":"http://arxiv.org/abs/1603.08482v1","url_pdf":"http://arxiv.org/pdf/1603.08482v1.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":"estimating-mixture-models-via-mixtures-of","repo_url":"https://github.com/sidaw/mompy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"estimating-mixture-models-via-mixtures-of","repo_url":"https://github.com/sidaw/polymom","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"estimating-mixture-models-via-mixtures-of","repo_url":"https://worksheets.codalab.org/worksheets/0xca42b883b1f9481989cfb02fe693649f","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}