{"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/learning-hmms-with-nonparametric-emissions","title":"Learning HMMs with Nonparametric Emissions via Spectral Decompositions of Continuous Matrices","arxiv_id":"1609.06390","date":"2016-09-21","proceeding":"NeurIPS 2016 12","authors":["Kirthevasan Kandasamy","Maruan Al-Shedivat","Eric P. Xing"],"abstract":"Recently, there has been a surge of interest in using spectral methods for\nestimating latent variable models. However, it is usually assumed that the\ndistribution of the observations conditioned on the latent variables is either\ndiscrete or belongs to a parametric family. In this paper, we study the\nestimation of an $m$-state hidden Markov model (HMM) with only smoothness\nassumptions, such as H\\\"olderian conditions, on the emission densities. By\nleveraging some recent advances in continuous linear algebra and numerical\nanalysis, we develop a computationally efficient spectral algorithm for\nlearning nonparametric HMMs. Our technique is based on computing an SVD on\nnonparametric estimates of density functions by viewing them as\n\\emph{continuous matrices}. We derive sample complexity bounds via\nconcentration results for nonparametric density estimation and novel\nperturbation theory results for continuous matrices. We implement our method\nusing Chebyshev polynomial approximations. Our method is competitive with other\nbaselines on synthetic and real problems and is also very computationally\nefficient.","url_abs":"http://arxiv.org/abs/1609.06390v1","url_pdf":"http://arxiv.org/pdf/1609.06390v1.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":"learning-hmms-with-nonparametric-emissions","repo_url":"https://github.com/alshedivat/nphmm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}