{"id":"https://openalex.org/W7225200577","doi":"https://doi.org/10.6084/m9.figshare.34894257","title":"Finite MMSE Data for Two-Component Gaussian Mixtures: Sharp Stability and Identifiability Obstructions","display_name":"Finite MMSE Data for Two-Component Gaussian Mixtures: Sharp Stability and Identifiability Obstructions","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225200577","doi":"https://doi.org/10.6084/m9.figshare.34894257"},"language":"en","primary_location":{"id":"doi:10.6084/m9.figshare.34894257","doi":"https://doi.org/10.6084/m9.figshare.34894257","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34894257","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.6084/m9.figshare.34894257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158201465","display_name":"Akihiro Koide","orcid":"https://orcid.org/0009-0002-8391-3480","observed_orcids":["https://orcid.org/0009-0002-8391-3480"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Akihiro Koide","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0002-8391-3480","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158201465"],"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9243000149726868,"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"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9243000149726868,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.0066999997943639755,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.006300000008195639,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/gaussian-mixture-model","display_name":"Gaussian mixture model","score":0.7170000076293945},{"id":"https://openalex.org/keywords/two-component-mixtures","display_name":"two-component mixtures","score":0.8550000190734863},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"minimum mean square error","score":0.8820000290870667},{"id":"https://openalex.org/keywords/identifiability","display_name":"identifiability","score":0.8289999961853027},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.6510000228881836},{"id":"https://openalex.org/keywords/transport-exponent","display_name":"transport exponent","score":0.5509999990463257},{"id":"https://openalex.org/keywords/cumulants","display_name":"cumulants","score":0.6179999709129333},{"id":"https://openalex.org/keywords/signal-to-noise-ratio-estimation","display_name":"signal-to-noise ratio estimation","score":0.5}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8859999775886536},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.6021000146865845},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5866000056266785},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.574400007724762},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.566100001335144},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5587999820709229},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4973999857902527},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41370001435279846},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4032999873161316},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3684999942779541},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.27410000562667847},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2632000148296356},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.6084/m9.figshare.34894257","doi":"https://doi.org/10.6084/m9.figshare.34894257","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34894257","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Preprint"},{"id":"doi:10.6084/m9.figshare.34894257.v1","doi":"https://doi.org/10.6084/m9.figshare.34894257.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34894257.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.6084/m9.figshare.34894257","doi":"https://doi.org/10.6084/m9.figshare.34894257","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34894257","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223318480","https://openalex.org/W4405240796","https://openalex.org/W2944668518","https://openalex.org/W2020609879","https://openalex.org/W2098581181","https://openalex.org/W2891574298","https://openalex.org/W2094541826","https://openalex.org/W7202196179","https://openalex.org/W7099279252","https://openalex.org/W7098777575"],"abstract_inverted_index":{"This":[0],"paper":[1,174],"studies":[2],"identification":[3,177,193,298],"and":[4,37,42,56,74,83,90,120,143,190,265,276,290,299],"inverse":[5,222,240],"stability":[6],"of":[7,20,32,140,216,246],"real":[8],"mixtures":[9],"with":[10,186,208],"at":[11,18,160],"most":[12],"two":[13,102,141,205],"Gaussian":[14,214],"components":[15],"from":[16,242,249],"derivatives":[17,31,210,248],"zero":[19,54],"their":[21],"Gaussian-channel":[22],"minimum":[23,139],"mean-square":[24],"error":[25],"(MMSE).":[26],"For":[27,197],"centered":[28],"symmetric":[29,192,275],"mixtures,":[30,199],"orders":[33],"zero,":[34],"three,":[35],"five,":[36],"six":[38,45,181],"determine":[39],"the":[40,59,75,97,113,127,138,144,151,161,164,170,230,260,284,293,305],"law,":[41],"maximum":[43],"order":[44,180,212],"is":[46,64,101,137,157,167,234,253],"necessary.":[47],"On":[48],"bounded":[49],"parameter":[50],"sets":[51],"that":[52],"allow":[53],"variances":[55],"vanishing":[57,187],"weights,":[58,96],"optimal":[60],"uniform":[61,221],"Holder":[62],"exponent":[63,100,130],"one":[65,105,118,121,226],"fourteenth":[66,119],"for":[67,182,283],"both":[68],"quadratic":[69],"Wasserstein":[70,76],"distance":[71,77],"between":[72,78],"laws":[73],"component":[79,115],"measures":[80],"in":[81,304],"mean":[82],"standard-deviation":[84],"coordinates.":[85],"With":[86],"positive":[87,134],"variance":[88,135,146,166],"bounds":[89],"a":[91,124,132,254,266,279],"lower":[92,171],"bound":[93,156],"on":[94,131],"nonzero":[95],"sharp":[98,128],"law":[99,129],"sevenths":[103,142],"or":[104],"third":[106,188],"according":[107],"to":[108,194],"an":[109,200],"explicit":[110],"weight":[111,125],"threshold;":[112],"corresponding":[114],"exponents":[116,223],"are":[117,302],"twelfth.":[122],"Without":[123],"floor,":[126],"fixed":[133],"band":[136],"upper":[145,165],"divided":[147],"by":[148],"four":[149],"times":[150,169],"variance-band":[152],"width.":[153],"The":[154,173,257,296],"endpoint":[155],"attained,":[158],"including":[159],"transition":[162],"where":[163],"eight":[168],"variance.":[172],"also":[175],"proves":[176],"through":[178,211],"derivative":[179,273],"every":[183],"two-component":[184],"mixture":[185],"cumulant":[189,288],"transfers":[191],"finite":[195,250],"projections.":[196],"nonsymmetric":[198],"exact":[201,243],"rational":[202,280],"certificate":[203,282],"constructs":[204],"distinct":[206],"distributions":[207],"identical":[209],"six.":[213],"smoothing":[215],"this":[217],"pair":[218],"rules":[219],"out":[220],"greater":[224],"than":[225],"quarter":[227],"even":[228],"when":[229],"entire":[231],"MMSE":[232],"curve":[233],"observed.":[235],"These":[236],"results":[237],"concern":[238],"deterministic":[239],"continuity":[241],"derivatives;":[244],"estimation":[245],"those":[247],"signal-to-noise":[251],"samples":[252],"separate":[255],"problem.":[256],"deposit":[258],"contains":[259],"manuscript":[261],"PDF,":[262],"LaTeX":[263],"source,":[264],"computation":[267],"supplement.":[268],"Seven":[269],"verification":[270],"programs":[271],"regenerate":[272],"polynomials,":[274],"weight-threshold":[277],"identities,":[278],"interval":[281],"sixth-order":[285],"collision,":[286],"independent":[287],"formulas,":[289],"identities":[291],"governing":[292],"transport":[294,300],"exponents.":[295],"analytic":[297],"arguments":[301],"proved":[303],"manuscript.":[306]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}