Identifiability of discrete Input-Output hidden Markov models with external signals

Identifiability of discrete Input-Output hidden Markov models with external signals | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Identifiability of discrete Input-Output hidden Markov models with external signals Étienne David, Jean Bellot, Sylvain Le Corff, Luc Lehéricy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2112123/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Dec, 2023 Read the published version in Statistics and Computing → Version 1 posted 7 You are reading this latest preprint version Abstract In this paper, we consider a bivariate process ( X t , Y t ) t∈Z which, conditionally on a signal ( W t ) t∈Z , is a hidden Markov model whose transition and emission kernels depend on ( Wt ) t∈Z. The resulting process ( X t , Y t , W t ) t∈Z is referred to as an input-output hidden Markov model or hidden Markov model with external signals. We prove that this model is identifiable and that the associated maximum likelihood estimator is consistent. Introducing an Expectation Maximization-based algorithm, we train and evaluate the performance of this model in several frameworks. In addition to learning dependencies between ( X t , Y t ) t∈Z and ( W t ) t∈Z , our approach based on hidden Markov models with external signals also outperforms state-of-the-art algorithms on real-world fashion sequences. Hidden Markov Model Identifiability Consistency Expectation-Maximization Fashion time series Full Text Additional Declarations No competing interests reported. Supplementary Files hmmwithexternalsignalssupplementarymaterial.zip Cite Share Download PDF Status: Published Journal Publication published 20 Dec, 2023 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Major revision 23 Apr, 2023 Reviews received at journal 20 Dec, 2022 Reviewers agreed at journal 24 Oct, 2022 Reviewers invited by journal 23 Oct, 2022 Editor assigned by journal 28 Sep, 2022 Submission checks completed at journal 28 Sep, 2022 First submitted to journal 28 Sep, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2112123","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":140276544,"identity":"8f4d1ffb-6ac8-4700-b3bd-35c96884ce4b","order_by":0,"name":"Étienne 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t∈Z , is a hidden Markov model whose transition and emission kernels depend on (\u003cem\u003e\u003cstrong\u003eWt\u003c/strong\u003e\u003c/em\u003e) t∈Z. The resulting process (\u003cem\u003e\u003cstrong\u003eX\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u003cstrong\u003e, Y\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u003cstrong\u003e, W\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e) t∈Z is referred to as an input-output hidden Markov model or hidden Markov model with external signals. We prove that this model is identifiable and that the associated maximum likelihood estimator is consistent. Introducing an Expectation Maximization-based algorithm, we train and evaluate the performance of this model in several frameworks. 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