{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T21:18:28Z","timestamp":1764364708816,"version":"3.44.0"},"reference-count":48,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"9","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["10.55776\/P35992","10.55776\/P33122","10.55776\/P34129"],"award-info":[{"award-number":["10.55776\/P35992","10.55776\/P33122","10.55776\/P34129"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Austrian Academy of Sciences (\u00d6AW) through DOC Scholarship","award":["26547"],"award-info":[{"award-number":["26547"]}]},{"name":"National Research, Development and Innovation Office","award":["KKP 137490"],"award-info":[{"award-number":["KKP 137490"]}]},{"name":"University of Innsbruck Early Stage Funding Program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1109\/tit.2025.3584695","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T13:37:51Z","timestamp":1751377071000},"page":"7052-7075","source":"Crossref","is-referenced-by-count":1,"title":["Hidden Markov Models and the Bayes Filter in Categorical Probability"],"prefix":"10.1109","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7081-2635","authenticated-orcid":false,"given":"Tobias","family":"Fritz","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Innsbruck, Innsbruck, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Klingler","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, University of Vienna, Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-2310-806X","authenticated-orcid":false,"given":"Drew","family":"McNeely","sequence":"additional","affiliation":[{"name":"Cockrell School of Engineering, The University of Texas at Austin, Austin, TX, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6830-9098","authenticated-orcid":false,"given":"Areeb","family":"Shah Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Innsbruck, Innsbruck, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3492-808X","authenticated-orcid":false,"given":"Yuwen","family":"Wang","sequence":"additional","affiliation":[{"name":"HUN-REN Alfr&#x00E9;d R&#x00E9;nyi Institute of Mathematics, Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"doi-asserted-by":"publisher","key":"ref1","DOI":"10.1007\/978-3-319-96131-6"},{"doi-asserted-by":"publisher","key":"ref2","DOI":"10.1007\/978-3-642-12821-9_2"},{"doi-asserted-by":"publisher","key":"ref3","DOI":"10.1002\/0471221279"},{"volume-title":"Factorization Methods for Discrete Sequential Estimation","year":"1977","author":"Bierman","key":"ref4"},{"doi-asserted-by":"publisher","key":"ref5","DOI":"10.1007\/BFb0120973"},{"key":"ref6","first-page":"13","article-title":"The entropy of functions of finite-state Markov chains","volume-title":"Proc. Trans. 1st Prague Conf. Inf. Theory, Czechoslovak Acad. Sci.","author":"Blackwell"},{"doi-asserted-by":"publisher","key":"ref7","DOI":"10.1007\/0-387-28982-8"},{"doi-asserted-by":"publisher","key":"ref8","DOI":"10.1214\/10-AAP688"},{"doi-asserted-by":"publisher","key":"ref9","DOI":"10.1017\/S0960129518000488"},{"doi-asserted-by":"publisher","key":"ref10","DOI":"10.1017\/9781316219317"},{"doi-asserted-by":"publisher","key":"ref11","DOI":"10.1007\/s11229-011-9917-5"},{"doi-asserted-by":"publisher","key":"ref12","DOI":"10.1016\/j.aim.2020.107239"},{"issue":"46","key":"ref13","first-page":"1","article-title":"The d-separation criterion in categorical probability","volume":"24","author":"Fritz","year":"2023","journal-title":"J. Mach. Learn. Res."},{"doi-asserted-by":"publisher","key":"ref14","DOI":"10.1007\/s10485-023-09717-0"},{"doi-asserted-by":"publisher","key":"ref15","DOI":"10.32408\/compositionality-2-3"},{"doi-asserted-by":"publisher","key":"ref16","DOI":"10.1016\/j.tcs.2023.113896"},{"key":"ref17","article-title":"Space-time tradeoffs of lenses and optics via higher category theory","author":"Gavranovi\u0107","year":"2022","journal-title":"arXiv:2209.09351"},{"doi-asserted-by":"publisher","key":"ref18","DOI":"10.1109\/TAC.1964.1105763"},{"volume-title":"Structured Probabilistic Reasoning","year":"2025","author":"Jacobs","key":"ref19"},{"doi-asserted-by":"publisher","key":"ref20","DOI":"10.1017\/CBO9780511790423"},{"doi-asserted-by":"publisher","key":"ref21","DOI":"10.1109\/JPROC.2003.823141"},{"doi-asserted-by":"publisher","key":"ref22","DOI":"10.1117\/12.280797"},{"doi-asserted-by":"publisher","key":"ref23","DOI":"10.1115\/1.3662552"},{"doi-asserted-by":"publisher","key":"ref24","DOI":"10.1115\/1.3658902"},{"doi-asserted-by":"publisher","key":"ref25","DOI":"10.1007\/BF00773470"},{"volume-title":"The Bayes Filter and Intro to State Estimation","year":"2018","author":"Lambert","key":"ref26"},{"doi-asserted-by":"publisher","key":"ref27","DOI":"10.1017\/CBO9781107360068"},{"doi-asserted-by":"publisher","key":"ref28","DOI":"10.23638\/LMCS-15(1:36)2019"},{"doi-asserted-by":"publisher","key":"ref29","DOI":"10.1109\/TAC.2018.2846684"},{"doi-asserted-by":"publisher","key":"ref30","DOI":"10.1214\/21-EJS1894"},{"volume-title":"Machine Learning: A Probabilistic Perspective","year":"2012","author":"Murphy","key":"ref31"},{"doi-asserted-by":"publisher","key":"ref32","DOI":"10.1142\/p595"},{"key":"ref33","doi-asserted-by":"crossref","DOI":"10.1142\/13670","volume-title":"Starting Category Theory","author":"Perrone","year":"2024"},{"doi-asserted-by":"publisher","key":"ref34","DOI":"10.1017\/9781009625715"},{"doi-asserted-by":"publisher","key":"ref35","DOI":"10.1007\/978-3-030-31175-9_19"},{"doi-asserted-by":"publisher","key":"ref36","DOI":"10.1109\/5.18626"},{"doi-asserted-by":"publisher","key":"ref37","DOI":"10.2514\/3.3166"},{"volume-title":"Beyond the Kalman Filter: Particle Filters for Tracking Applications","year":"2004","author":"Ristic","key":"ref38"},{"doi-asserted-by":"publisher","key":"ref39","DOI":"10.1162\/089976699300016674"},{"doi-asserted-by":"publisher","key":"ref40","DOI":"10.1017\/CBO9781139344203"},{"key":"ref41","article-title":"Compositionality in algorithms for smoothing","author":"Schauer","year":"2023","journal-title":"arXiv:2303.13865"},{"doi-asserted-by":"publisher","key":"ref42","DOI":"10.1007\/0-387-32792-4"},{"volume-title":"Github Project: Markov Categories in C++","year":"2024","author":"Soloviev","key":"ref43"},{"key":"ref44","first-page":"13:1","article-title":"A category for unifying Gaussian probability and nondeterminism","volume-title":"Proc. CALCO","volume":"270","author":"Stein"},{"volume-title":"The C++ Programming Language","year":"2013","author":"Stroustrup","key":"ref45"},{"key":"ref46","article-title":"Active inference in string diagrams: A categorical account of predictive processing and free energy","author":"Tull","year":"2023","journal-title":"arXiv:2308.00861"},{"key":"ref47","article-title":"Automatic backward filtering forward guiding for Markov processes and graphical models","author":"van der Meulen","year":"2020","journal-title":"arXiv:2010.03509"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"299","DOI":"10.4204\/EPTCS.397.18","article-title":"Unifilar machines and the adjoint structure of Bayesian models","volume":"397","author":"Virgo","year":"2023","journal-title":"EPTCS"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/18\/11134633\/11062600.pdf?arnumber=11062600","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T20:44:29Z","timestamp":1756154669000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11062600\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":48,"journal-issue":{"issue":"9"},"URL":"https:\/\/doi.org\/10.1109\/tit.2025.3584695","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"type":"print","value":"0018-9448"},{"type":"electronic","value":"1557-9654"}],"subject":[],"published":{"date-parts":[[2025,9]]}}}