{"id":"https://openalex.org/W7154457840","doi":"https://doi.org/10.48550/arxiv.2604.12334","title":"On additive averaging kernels for finite Markov chains","display_name":"On additive averaging kernels for finite Markov chains","publication_year":2026,"publication_date":"2026-04-14","ids":{"openalex":"https://openalex.org/W7154457840","doi":"https://doi.org/10.48550/arxiv.2604.12334"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.12334","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.12334","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.12334","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133692699","display_name":"Ryan J. Y. Lim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lim, Ryan J. Y.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058187515","display_name":"Michael C. H. Choi","orcid":"https://orcid.org/0000-0003-0309-3217"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choi, Michael C. H.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5133692699"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.8896999955177307,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.8896999955177307,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.023499999195337296,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.01899999938905239,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6837999820709229},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.5343000292778015},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5291000008583069},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4447999894618988},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4097999930381775},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.40779998898506165},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.37549999356269836},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.3587999939918518}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7821000218391418},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6837999820709229},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4447999894618988},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.430400013923645},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4097999930381775},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.40779998898506165},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.32739999890327454},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3073999881744385},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C203223496","wikidata":"https://www.wikidata.org/wiki/Q4681344","display_name":"Additive model","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2736999988555908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2667999863624573},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2547000050544739},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.12334","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.12334","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.12334","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.12334","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,36,55,111,182],"study":[1,40],"additive":[2],"mixtures":[3],"of":[4,7,32,41,50,60,123,137,143,166,196],"Markov":[5,53],"kernels":[6],"the":[8,33,39,48,58,67,72,77,119,126,135,153,159,168,171,199],"form":[9],"$A_\u03b1=":[10],"\u03b1P":[11],"+":[12],"(1-\u03b1)G$,":[13],"where":[14],"$\u03b1\\in":[15],"[0,1]$,":[16],"$P$":[17,145],"is":[18,24,139],"a":[19,25,30,51,87,97,103,184],"baseline":[20],"sampler":[21],"and":[22,71,85,146,170,190],"$G$":[23],"Gibbs":[26,154],"kernel":[27],"induced":[28],"by":[29,118,141],"partition":[31,150,169],"state":[34],"space.":[35],"first":[37],"motivate":[38],"$A_\u03b1$,":[42],"which":[43],"can":[44,174],"be":[45],"interpreted":[46],"as":[47],"projection":[49],"lifted":[52],"chain.":[54],"then":[56],"consider":[57],"minimisation":[59],"distance":[61],"to":[62,152],"stationarity":[63],"under":[64],"two":[65],"objectives:":[66],"squared":[68],"Frobenius":[69,78],"norm":[70],"Kullback-Leibler":[73],"(KL)":[74],"divergence.":[75],"For":[76,125],"objective,":[79],"we":[80,129],"derive":[81],"explicit":[82],"trace":[83],"formulas":[84],"identify":[86],"Cheeger-type":[88],"functional":[89],"that":[90,134,163],"characterises":[91],"optimal":[92],"two-block":[93],"partitions.":[94],"This":[95],"yields":[96],"structured":[98],"combinatorial":[99],"optimisation":[100],"problem":[101],"admitting":[102],"difference-of-submodular":[104],"decomposition,":[105],"enabling":[106],"efficient":[107],"approximation":[108],"via":[109],"majorisation-minimisation.":[110],"also":[112],"obtain":[113],"geometric":[114],"decay":[115],"rates":[116],"governed":[117],"absolute":[120],"spectral":[121],"gap":[122],"$P$.":[124],"KL":[127],"divergence,":[128],"establish":[130],"convexity-based":[131],"bounds":[132],"showing":[133],"divergence":[136],"$A_\u03b1$":[138],"controlled":[140],"those":[142],"both":[144,167],"$G$,":[147],"thereby":[148],"reducing":[149],"selection":[151],"component.":[155],"Numerical":[156],"experiments":[157],"on":[158],"Curie-Weiss":[160],"model":[161],"demonstrate":[162],"suitable":[164],"choice":[165],"parameter":[172],"$\u03b1$":[173,197],"significantly":[175],"accelerate":[176],"convergence":[177],"in":[178],"total":[179],"variation":[180],"distance.":[181],"observe":[183],"consistent":[185],"trade-off":[186],"between":[187],"local":[188],"exploration":[189],"global":[191],"averaging,":[192],"with":[193],"intermediate":[194],"values":[195],"achieving":[198],"best":[200],"performance":[201],"across":[202],"regimes.":[203]},"counts_by_year":[],"updated_date":"2026-04-16T06:09:31.884825","created_date":"2026-04-16T00:00:00"}