{"id":"https://openalex.org/W4415524348","doi":"https://doi.org/10.1109/mlsp62443.2025.11204343","title":"HESS-MC <sup>2</sup> : Sequential Monte Carlo Squared Using Hessian Information and Second Order Proposals","display_name":"HESS-MC <sup>2</sup> : Sequential Monte Carlo Squared Using Hessian Information and Second Order Proposals","publication_year":2025,"publication_date":"2025-08-31","ids":{"openalex":"https://openalex.org/W4415524348","doi":"https://doi.org/10.1109/mlsp62443.2025.11204343"},"language":null,"primary_location":{"id":"doi:10.1109/mlsp62443.2025.11204343","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp62443.2025.11204343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 35th International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007595974","display_name":"Joshua Murphy","orcid":"https://orcid.org/0000-0001-9085-5755"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Joshua Murphy","raw_affiliation_strings":["University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003665024","display_name":"Conor Rosato","orcid":"https://orcid.org/0000-0001-8394-7344"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Conor Rosato","raw_affiliation_strings":["University of Liverpool,Department of Pharmacology and Therapeutics,United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool,Department of Pharmacology and Therapeutics,United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008594180","display_name":"Andrew R. Millard","orcid":"https://orcid.org/0000-0002-8290-7428"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew Millard","raw_affiliation_strings":["University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090760798","display_name":"Lee Devlin","orcid":"https://orcid.org/0000-0002-2059-7284"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lee Devlin","raw_affiliation_strings":["University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067315679","display_name":"Paul Horridge","orcid":"https://orcid.org/0009-0005-9381-3557"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paul Horridge","raw_affiliation_strings":["University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083636287","display_name":"Simon Maskell","orcid":"https://orcid.org/0000-0003-1917-2913"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Simon Maskell","raw_affiliation_strings":["University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool,Department of Electrical Engineering and Electronics,United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":null,"apc_paid":null,"fwci":2.5112,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.90346717,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.41609999537467957,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.41609999537467957,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.35519999265670776,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.3517000079154968,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.7558000087738037},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7434999942779541},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.7092000246047974},{"id":"https://openalex.org/keywords/particle-filter","display_name":"Particle filter","score":0.6679999828338623},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.5527999997138977},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.4943999946117401},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.41839998960494995},{"id":"https://openalex.org/keywords/approximate-inference","display_name":"Approximate inference","score":0.40880000591278076},{"id":"https://openalex.org/keywords/monte-carlo-molecular-modeling","display_name":"Monte Carlo molecular modeling","score":0.4043000042438507}],"concepts":[{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.7558000087738037},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7434999942779541},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7092000246047974},{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.6679999828338623},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.5527999997138977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49900001287460327},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49549999833106995},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.4943999946117401},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42590001225471497},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.40880000591278076},{"id":"https://openalex.org/C37669827","wikidata":"https://www.wikidata.org/wiki/Q6904703","display_name":"Monte Carlo molecular modeling","level":4,"score":0.4043000042438507},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3921999931335449},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.38929998874664307},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.37450000643730164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36640000343322754},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.34619998931884766},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C204493344","wikidata":"https://www.wikidata.org/wiki/Q6904698","display_name":"Monte Carlo method in statistical physics","level":5,"score":0.3098999857902527},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.28220000863075256},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.2648000121116638}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/mlsp62443.2025.11204343","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp62443.2025.11204343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 35th International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1054226923","display_name":null,"funder_award_id":"226691/Z/22/Z","funder_id":"https://openalex.org/F4320311904","funder_display_name":"Wellcome Trust"},{"id":"https://openalex.org/G4860320577","display_name":"Big Hypotheses: A Fully Parallelised Bayesian Inference Solution","funder_award_id":"EP/R018537/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320311904","display_name":"Wellcome Trust","ror":"https://ror.org/029chgv08"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1545319692","https://openalex.org/W1876120984","https://openalex.org/W1983452151","https://openalex.org/W2051768929","https://openalex.org/W2059535441","https://openalex.org/W2147357149","https://openalex.org/W2153181693","https://openalex.org/W2160337655","https://openalex.org/W2165218107","https://openalex.org/W2271646078","https://openalex.org/W2962739356","https://openalex.org/W2963872333","https://openalex.org/W3211330167","https://openalex.org/W3215540479","https://openalex.org/W4293252589","https://openalex.org/W4293775970","https://openalex.org/W4390044799","https://openalex.org/W4390445385","https://openalex.org/W4394586038","https://openalex.org/W4403278291","https://openalex.org/W4413679297"],"related_works":[],"abstract_inverted_index":{"When":[0],"performing":[1],"Bayesian":[2],"inference":[3],"using":[4],"Sequential":[5,26],"Monte":[6,27,111],"Carlo":[7,28,112],"(SMC)":[8],"methods,":[9,114],"two":[10],"considerations":[11],"arise:":[12],"the":[13,16,41,50,95,98,117,123,130,136,141,150],"accuracy":[14,46,163],"of":[15,40,49,80,97,140,152,157],"posterior":[17,51,161],"approximation":[18,162],"and":[19,47,63,160],"computational":[20,24],"efficiency.":[21],"To":[22],"address":[23],"demands,":[25],"Squared":[29],"(SMC${}^{2}$)":[30],"is":[31],"well-suited":[32],"for":[33],"high-performance":[34],"computing":[35],"(HPC)":[36],"environments.":[37],"The":[38,66],"design":[39],"proposal":[42],"distribution":[43],"within$\\text{SMC}^{2}$can":[44],"improve":[45],"exploration":[48],"as":[52],"poor":[53],"proposals":[54,102,126],"may":[55],"lead":[56],"to":[57,119,166],"high":[58],"variance":[59],"in":[60,107,155],"importance":[61],"weights":[62],"particle":[64,108],"degeneracy.":[65],"Metropolis-Adjusted":[67],"Langevin":[68],"Algorithm":[69],"(MALA)":[70],"uses":[71],"gradient":[72,131],"information":[73],"so":[74],"that":[75],"particles":[76],"preferentially":[77],"explore":[78],"regions":[79],"higher":[81],"probability.":[82],"In":[83],"this":[84,88],"paper,":[85],"we":[86,115],"extend":[87],"idea":[89],"by":[90],"incorporating":[91],"second-order":[92,101],"information,":[93],"specifically":[94],"Hessian":[96],"log-target.":[99],"While":[100],"have":[103],"been":[104],"explored":[105],"previously":[106],"Markov":[109],"Chain":[110],"(p-MCMC)":[113],"are":[116],"first":[118],"introduce":[120],"them":[121],"within":[122],"SMC2framework.":[124],"Second-order":[125],"not":[127],"only":[128],"use":[129],"(first-order":[132],"derivative),":[133],"but":[134],"also":[135],"curvature":[137],"(second-order":[138],"derivative)":[139],"target":[142],"distribution.":[143],"Experimental":[144],"results":[145],"on":[146],"synthetic":[147],"models":[148],"highlight":[149],"benefits":[151],"our":[153],"approach":[154],"terms":[156],"step-size":[158],"selection":[159],"when":[164],"compared":[165],"other":[167],"proposals.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-24T00:00:00"}
