{"id":"https://openalex.org/W7215837866","doi":"https://doi.org/10.48550/arxiv.2610.02128","title":"Sample complexity bounds for categorical Markov random fields via Discrete Diffusions","display_name":"Sample complexity bounds for categorical Markov random fields via Discrete Diffusions","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7215837866","doi":"https://doi.org/10.48550/arxiv.2610.02128"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02128","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02128","pdf_url":"https://arxiv.org/pdf/2610.02128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02128","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5154350455","display_name":"Shivam Kumar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kumar, Shivam","raw_affiliation_strings":["Booth School of Business , University of Chicago ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Booth School of Business , University of Chicago ,","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024944074","display_name":"Nabarun Deb","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deb, Nabarun","raw_affiliation_strings":["Booth School of Business , University of Chicago ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Booth School of Business , University of Chicago ,","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9951000213623047,"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":0.9951000213623047,"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":0.000699999975040555,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.0006000000284984708,"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/discrete-diffusion","display_name":"discrete diffusion","score":0.7850000262260437},{"id":"https://openalex.org/keywords/sample-complexity-bounds","display_name":"sample complexity bounds","score":0.7559999823570251},{"id":"https://openalex.org/keywords/tau-leaping","display_name":"tau-leaping","score":0.8199999928474426},{"id":"https://openalex.org/keywords/local-dependence","display_name":"local dependence","score":0.6430000066757202},{"id":"https://openalex.org/keywords/potts-model","display_name":"Potts model","score":0.7300000190734863},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.9980000257492065},{"id":"https://openalex.org/keywords/tree-based-models","display_name":"tree-based models","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.6128000020980835},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5361999869346619},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.412200003862381},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4000999927520752},{"id":"https://openalex.org/C170593435","wikidata":"https://www.wikidata.org/wiki/Q4128565","display_name":"Slice sampling","level":4,"score":0.39340001344680786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3880999982357025},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.382099986076355},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.3790000081062317},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3763999938964844},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C39943821","wikidata":"https://www.wikidata.org/wiki/Q506346","display_name":"Semimartingale","level":2,"score":0.3393999934196472},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3230000138282776},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32170000672340393},{"id":"https://openalex.org/C110384440","wikidata":"https://www.wikidata.org/wiki/Q1143270","display_name":"Upsampling","level":3,"score":0.31949999928474426},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C2779377595","wikidata":"https://www.wikidata.org/wiki/Q21045424","display_name":"Approximate Bayesian computation","level":3,"score":0.28630000352859497},{"id":"https://openalex.org/C20353970","wikidata":"https://www.wikidata.org/wiki/Q1056998","display_name":"Simple random sample","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C20326153","wikidata":"https://www.wikidata.org/wiki/Q7049638","display_name":"Nonuniform sampling","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.26109999418258667},{"id":"https://openalex.org/C82152865","wikidata":"https://www.wikidata.org/wiki/Q7208505","display_name":"Poisson sampling","level":5,"score":0.25999999046325684},{"id":"https://openalex.org/C167927819","wikidata":"https://www.wikidata.org/wiki/Q1930567","display_name":"Shuffling","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.25290000438690186},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02128","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02128","pdf_url":"https://arxiv.org/pdf/2610.02128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.02128","doi":"https://doi.org/10.48550/arxiv.2610.02128","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02128","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02128","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02128","pdf_url":"https://arxiv.org/pdf/2610.02128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215837866.pdf","grobid_xml":"https://content.openalex.org/works/W7215837866.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W2064675550","https://openalex.org/W2068674173","https://openalex.org/W2112796928","https://openalex.org/W2114220616","https://openalex.org/W2159793005","https://openalex.org/W3003409689","https://openalex.org/W3039256091","https://openalex.org/W3201938571","https://openalex.org/W4245577611","https://openalex.org/W4391462055","https://openalex.org/W4403884736","https://openalex.org/W4404167116","https://openalex.org/W4404352484","https://openalex.org/W4404987740","https://openalex.org/W4406093376","https://openalex.org/W4406949304","https://openalex.org/W4407123380","https://openalex.org/W4407569673","https://openalex.org/W4407679583","https://openalex.org/W4408272963","https://openalex.org/W4414690724","https://openalex.org/W4414745219","https://openalex.org/W4415037548","https://openalex.org/W4415156275","https://openalex.org/W4415249999","https://openalex.org/W4416027183","https://openalex.org/W4416051103","https://openalex.org/W4416113503","https://openalex.org/W4416953122","https://openalex.org/W6967055661","https://openalex.org/W7090709548","https://openalex.org/W7104261662","https://openalex.org/W7129339926","https://openalex.org/W7131816111","https://openalex.org/W7131820717","https://openalex.org/W7152097927","https://openalex.org/W7161724837","https://openalex.org/W7162561378","https://openalex.org/W7203478542","https://openalex.org/W7204147297","https://openalex.org/W7204176442","https://openalex.org/W7204876163","https://openalex.org/W7207851285"],"related_works":["https://openalex.org/W7129339926","https://openalex.org/W2803279263","https://openalex.org/W7204176442","https://openalex.org/W4407633238","https://openalex.org/W7090709548","https://openalex.org/W4406949304","https://openalex.org/W4407684131","https://openalex.org/W4310558019","https://openalex.org/W4407570924","https://openalex.org/W4380994591"],"abstract_inverted_index":{"Many":[0],"applications":[1],"in":[2,27,102,157],"statistics,":[3],"economics,":[4],"and":[5,24,30,134,170,188,235],"physics":[6,29],"require":[7],"sampling":[8,47,143,159,173,207,248],"from":[9,117,167],"high-dimensional":[10],"categorical":[11],"distributions":[12],"with":[13,50,61,69,137,175],"local":[14,73],"dependence":[15,112,119,177],"structures.":[16],"Examples":[17],"include":[18],"finite":[19,168],"memory":[20],"language":[21],"models,":[22],"Ising":[23],"Potts":[25],"systems":[26],"statistical":[28],"protein":[31],"folding,":[32],"etc.":[33],"In":[34],"modern":[35],"machine":[36],"learning,":[37],"discrete":[38,67,96],"diffusions":[39],"have":[40],"emerged":[41],"as":[42,150,154,226],"a":[43,90,129,151,196],"flexible":[44],"approach":[45],"for":[46,66,223,247],"such":[48],"data,":[49],"strong":[51],"empirical":[52],"performance.":[53],"Motivated":[54],"by":[55],"this,":[56],"we":[57,76,127,161],"develop":[58],"learning":[59,165],"methods":[60],"end-to-end":[62,142],"sample":[63,190],"complexity":[64],"bounds":[65],"diffusion":[68],"uniform":[70,201],"noising":[71],"under":[72],"dependence,":[74],"which":[75],"model":[77,219],"through":[78],"low":[79],"order":[80,184],"Markov":[81],"random":[82],"fields":[83],"(MRFs).":[84],"Our":[85],"main":[86],"technical":[87],"insight":[88],"is":[89,155],"new":[91],"\\emph{pinning":[92],"decomposition}":[93],"of":[94,185],"the":[95,105,111,118,121,163,179,182,186,189,206,216],"score.":[97],"It":[98],"shows":[99],"that":[100,239],"unlike":[101],"continuous":[103],"diffusions,":[104],"score":[106,132,164,198,241],"decomposes":[107],"into":[108],"components":[109],"where":[110],"on":[113,120,124,178,232],"time":[114],"separates":[115],"multiplicatively":[116],"target.":[122],"Building":[123],"this":[125],"decomposition,":[126],"propose":[128],"\\emph{weight-sharing":[130],"neural":[131],"learner}":[133],"combine":[135],"it":[136],"$\u03c4$-leaping":[138],"to":[139,209,220],"obtain":[140],"an":[141],"procedure.":[144],"Rather":[145],"than":[146],"treating":[147],"score-learning":[148],"error":[149,166],"black-box":[152],"input,":[153],"common":[156],"existing":[158],"analyses,":[160],"study":[162],"data":[169],"derive":[171],"optimal":[172],"guarantees":[174],"explicit":[176],"vocabulary":[180],"size,":[181],"interaction":[183],"MRF,":[187],"size.":[191],"Moreover,":[192],"our":[193],"strategy":[194],"trains":[195],"single":[197],"network":[199],"across":[200],"noise":[202],"levels":[203],"while":[204],"leaving":[205],"discretization":[208],"be":[210],"chosen":[211],"at":[212],"inference-time.":[213],"This":[214],"allows":[215],"same":[217],"trained":[218],"trade":[221],"accuracy":[222],"computational":[224],"cost":[225],"inference-time":[227],"budgets":[228],"vary.":[229],"Numerical":[230],"experiments":[231],"Potts,":[233],"Ising,":[234],"tree-structured":[236],"models":[237],"show":[238],"weight-sharing":[240],"networks":[242],"outperform":[243],"fully":[244],"connected":[245],"ones":[246],"long":[249],"sequences.":[250]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}