{"id":"https://openalex.org/W7204818066","doi":"https://doi.org/10.48550/arxiv.2608.27705","title":"On the Computational and Statistical Efficiency of the Empirical Maximum Entropy on the Mean Method","display_name":"On the Computational and Statistical Efficiency of the Empirical Maximum Entropy on the Mean Method","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204818066","doi":"https://doi.org/10.48550/arxiv.2608.27705"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27705","pdf_url":"https://arxiv.org/pdf/2608.27705","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/2608.27705","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016554146","display_name":"Matthew King\u2013Roskamp","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"King-Roskamp, Matthew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044688945","display_name":"Gabriel Rioux","orcid":"https://orcid.org/0000-0003-2244-9506","observed_orcids":["https://orcid.org/0000-0003-2244-9506"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rioux, Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058698689","display_name":"Rustum Choksi","orcid":"https://orcid.org/0000-0003-2419-9520","observed_orcids":["https://orcid.org/0000-0003-2419-9520"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choksi, Rustum","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000608751","display_name":"Tim Hoheisel","orcid":"https://orcid.org/0000-0002-0782-6302","observed_orcids":["https://orcid.org/0000-0002-0782-6302"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hoheisel, Tim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.004800000227987766,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0013000000035390258,"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/inverse-problems","display_name":"inverse problems","score":0.9700000286102295},{"id":"https://openalex.org/keywords/data-driven-priors","display_name":"data-driven priors","score":0.6769999861717224},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.8149999976158142},{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.6589999794960022},{"id":"https://openalex.org/keywords/primal-dual-optimization","display_name":"primal-dual optimization","score":0.8100000023841858},{"id":"https://openalex.org/keywords/expected-risk-minimization","display_name":"expected risk minimization","score":0.9739999771118164},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"stochastic optimization","score":0.8650000095367432},{"id":"https://openalex.org/keywords/stochastic-gradient-methods","display_name":"stochastic gradient algorithm","score":0.7829999923706055},{"id":"https://openalex.org/keywords/large-scale-inverse-problems","display_name":"large-scale inverse problems","score":0.8309999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6011000275611877},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.560699999332428},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.5109999775886536},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43320000171661377},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4296000003814697},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4169999957084656},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4090000092983246},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.383899986743927},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3776000142097473},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.3203999996185303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.313400000333786},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.29910001158714294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2978000044822693},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27705","pdf_url":"https://arxiv.org/pdf/2608.27705","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.2608.27705","doi":"https://doi.org/10.48550/arxiv.2608.27705","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27705","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:2608.27705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27705","pdf_url":"https://arxiv.org/pdf/2608.27705","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":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204818066.pdf","grobid_xml":"https://content.openalex.org/works/W7204818066.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7128674960","https://openalex.org/W4406067488","https://openalex.org/W7098187402","https://openalex.org/W7098486046","https://openalex.org/W7098197432","https://openalex.org/W1968379110","https://openalex.org/W1589292323","https://openalex.org/W173480056","https://openalex.org/W1995790726","https://openalex.org/W7095853108"],"abstract_inverted_index":{"The":[0],"Maximum":[1],"Entropy":[2],"on":[3,75,96],"the":[4,27,42,61,81,90,108,125],"Mean":[5],"(MEM)":[6],"method":[7],"provides":[8],"a":[9,48,76,113,148],"flexible":[10],"computational":[11],"framework":[12,127],"for":[13,56,137,154],"solving":[14],"inverse":[15,139,156],"problems":[16,86],"by":[17,66],"combining":[18],"data":[19],"fidelity":[20],"with":[21],"entropy-based":[22],"regularization.":[23],"In":[24],"practice,":[25],"however,":[26],"prior":[28],"distribution":[29],"is":[30,73],"typically":[31],"unknown":[32],"but":[33],"can":[34],"be":[35],"estimated":[36],"from":[37,99],"data,":[38],"giving":[39],"rise":[40],"to":[41],"empirical":[43,57,145],"MEM":[44,109,123,146],"method.":[45],"We":[46,104],"establish":[47],"parametric":[49],"convergence":[50],"rate":[51],"of":[52,80,89,128],"$O(n^{-1/2})$":[53],"in":[54],"expectation":[55],"MEM,":[58],"improving":[59],"upon":[60],"previously":[62],"established":[63],"$O(n^{-1/4})$":[64],"guarantee":[65],"King-Roskamp":[67],"et":[68],"al.":[69],"(2026).":[70],"Our":[71],"proof":[72],"based":[74],"novel":[77],"stability":[78],"analysis":[79,101],"primal":[82],"and":[83,102,131,150],"dual":[84,110],"optimization":[85,130],"under":[87],"perturbations":[88],"underlying":[91],"probability":[92],"measure,":[93],"relying":[94],"only":[95],"foundational":[97],"tools":[98],"convex":[100],"probability.":[103],"further":[105],"show":[106],"that":[107],"problem":[111],"admits":[112],"reformulation":[114],"as":[115,147],"an":[116],"expected":[117],"risk":[118],"minimization":[119],"problem,":[120],"thereby":[121],"placing":[122],"within":[124],"modern":[126],"stochastic":[129,134],"enabling":[132],"scalable":[133],"gradient":[135],"algorithms":[136],"large-scale":[138],"problems.":[140,157],"Together,":[141],"these":[142],"results":[143],"place":[144],"statistically":[149],"computationally":[151],"efficient":[152],"methodology":[153],"data-driven":[155]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-01T00:00:00"}