{"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/implementing-spectral-methods-for-hidden","title":"Implementing spectral methods for hidden Markov models with real-valued emissions","arxiv_id":"1404.7472","date":"2014-04-29","proceeding":null,"authors":["Carl Mattfeld"],"abstract":"Hidden Markov models (HMMs) are widely used statistical models for modeling\nsequential data. The parameter estimation for HMMs from time series data is an\nimportant learning problem. The predominant methods for parameter estimation\nare based on local search heuristics, most notably the expectation-maximization\n(EM) algorithm. These methods are prone to local optima and oftentimes suffer\nfrom high computational and sample complexity. Recent years saw the emergence\nof spectral methods for the parameter estimation of HMMs, based on a method of\nmoments approach. Two spectral learning algorithms as proposed by Hsu, Kakade\nand Zhang 2012 (arXiv:0811.4413) and Anandkumar, Hsu and Kakade 2012\n(arXiv:1203.0683) are assessed in this work. Using experiments with synthetic\ndata, the algorithms are compared with each other. Furthermore, the spectral\nmethods are compared to the Baum-Welch algorithm, a well-established method\napplying the EM algorithm to HMMs. The spectral algorithms are found to have a\nmuch more favorable computational and sample complexity. Even though the\nalgorithms readily handle high dimensional observation spaces, instability\nissues are encountered in this regime. In view of learning from real-world\nexperimental data, the representation of real-valued observations for the use\nin spectral methods is discussed, presenting possible methods to represent data\nfor the use in the learning algorithms.","url_abs":"http://arxiv.org/abs/1404.7472v1","url_pdf":"http://arxiv.org/pdf/1404.7472v1.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":"implementing-spectral-methods-for-hidden","repo_url":"https://github.com/cmgithub/spectral","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}