{"id":"https://openalex.org/W2203957096","doi":"https://doi.org/10.1162/neco_a_00804","title":"Mutual Information, Fisher Information, and Efficient Coding","display_name":"Mutual Information, Fisher Information, and Efficient Coding","publication_year":2015,"publication_date":"2015-12-14","ids":{"openalex":"https://openalex.org/W2203957096","doi":"https://doi.org/10.1162/neco_a_00804","mag":"2203957096","pmid":"https://pubmed.ncbi.nlm.nih.gov/26654209"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00804","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00804","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5003487806","display_name":"Xue-Xin Wei","orcid":"https://orcid.org/0000-0002-2761-477X"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xue-Xin Wei","raw_affiliation_strings":["Department of Psychology, University of Pennsylvania, Philadelphia, PA 19104, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychology, University of Pennsylvania, Philadelphia, PA 19104, U.S.A","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042556986","display_name":"Alan A. Stocker","orcid":"https://orcid.org/0000-0002-2041-1515"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]},{"id":"https://openalex.org/I922845939","display_name":"Philadelphia University","ror":"https://ror.org/03zzmyz63","country_code":"US","type":"education","lineage":["https://openalex.org/I922845939"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alan A. Stocker","raw_affiliation_strings":["Departments of Psychology and Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Psychology and Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, U.S.A","institution_ids":["https://openalex.org/I79576946","https://openalex.org/I922845939"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003487806","https://openalex.org/A5042556986"],"corresponding_institution_ids":["https://openalex.org/I79576946","https://openalex.org/I922845939"],"apc_list":null,"apc_paid":null,"fwci":1.9576,"has_fulltext":false,"cited_by_count":93,"citation_normalized_percentile":{"value":0.85907176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"28","issue":"2","first_page":"305","last_page":"326"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10448","display_name":"Memory and Neural Mechanisms","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.858954906463623},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.7932888269424438},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.6567986607551575},{"id":"https://openalex.org/keywords/neural-coding","display_name":"Neural coding","score":0.6449829936027527},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5837521553039551},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5106757283210754},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.483551949262619},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45008131861686707},{"id":"https://openalex.org/keywords/fisher-kernel","display_name":"Fisher kernel","score":0.4301249384880066},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38440877199172974},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3695979118347168},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3515908718109131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3413892984390259},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3360760807991028},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24472051858901978}],"concepts":[{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.858954906463623},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.7932888269424438},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.6567986607551575},{"id":"https://openalex.org/C77637269","wikidata":"https://www.wikidata.org/wiki/Q7002051","display_name":"Neural coding","level":2,"score":0.6449829936027527},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5837521553039551},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5106757283210754},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.483551949262619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45008131861686707},{"id":"https://openalex.org/C207798031","wikidata":"https://www.wikidata.org/wiki/Q8563425","display_name":"Fisher kernel","level":5,"score":0.4301249384880066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38440877199172974},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3695979118347168},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3515908718109131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3413892984390259},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3360760807991028},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24472051858901978},{"id":"https://openalex.org/C31510193","wikidata":"https://www.wikidata.org/wiki/Q1192553","display_name":"Facial recognition system","level":3,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C181367576","wikidata":"https://www.wikidata.org/wiki/Q6394184","display_name":"Kernel Fisher discriminant analysis","level":4,"score":0.0}],"mesh":[{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007257","descriptor_name":"Information Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007257","descriptor_name":"Information Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007257","descriptor_name":"Information Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_a_00804","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00804","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:26654209","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26654209","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W81409850","https://openalex.org/W1471548710","https://openalex.org/W1496712726","https://openalex.org/W1528822345","https://openalex.org/W1573082642","https://openalex.org/W1938985748","https://openalex.org/W1964291102","https://openalex.org/W1965555277","https://openalex.org/W1970792572","https://openalex.org/W1972287225","https://openalex.org/W1984931175","https://openalex.org/W1992145073","https://openalex.org/W1993197592","https://openalex.org/W1995875735","https://openalex.org/W2041905826","https://openalex.org/W2043371182","https://openalex.org/W2052036764","https://openalex.org/W2056129277","https://openalex.org/W2058598594","https://openalex.org/W2068782468","https://openalex.org/W2077554996","https://openalex.org/W2082195896","https://openalex.org/W2084840427","https://openalex.org/W2088400612","https://openalex.org/W2092170739","https://openalex.org/W2099111195","https://openalex.org/W2103234826","https://openalex.org/W2103236816","https://openalex.org/W2105848238","https://openalex.org/W2108384452","https://openalex.org/W2121881115","https://openalex.org/W2122741244","https://openalex.org/W2122759946","https://openalex.org/W2122925692","https://openalex.org/W2139704385","https://openalex.org/W2143990419","https://openalex.org/W2160570986","https://openalex.org/W2166405697","https://openalex.org/W2168544128","https://openalex.org/W2170334989","https://openalex.org/W2171185086","https://openalex.org/W2210387432","https://openalex.org/W2596585349","https://openalex.org/W2604272474","https://openalex.org/W2993383518","https://openalex.org/W4205125306","https://openalex.org/W4213348475","https://openalex.org/W4229633200","https://openalex.org/W4231370560","https://openalex.org/W4234824781"],"related_works":["https://openalex.org/W3185610468","https://openalex.org/W4294328901","https://openalex.org/W2952582351","https://openalex.org/W3138843862","https://openalex.org/W2042150869","https://openalex.org/W2114041665","https://openalex.org/W4380714911","https://openalex.org/W1997501514","https://openalex.org/W2964004529","https://openalex.org/W2203957096"],"abstract_inverted_index":{"Fisher":[0,56,77,154,170],"information":[1,12,57,78,139,171],"is":[2,20,40,72,105,181],"generally":[3],"believed":[4],"to":[5,75,130],"represent":[6],"a":[7,17,84,141,148,158],"lower":[8],"bound":[9,62,85],"on":[10,63,86,190],"mutual":[11,64,87,138],"(Brunel":[13],"&":[14],"Nadal,":[15],"1998),":[16],"result":[18],"that":[19,33,50,70,188,200,211],"frequently":[21],"used":[22],"in":[23,51,151],"the":[24,34,52,92,95,99,103,116,132,145,165,168,173,176,194],"assessment":[25],"of":[26,136,147,153,160,175,207,218],"neural":[27,112,119,149,195,209],"coding":[28,113,121,134,162],"efficiency.":[29],"However,":[30],"we":[31,48],"demonstrate":[32,199],"relation":[35],"between":[36,94,118,140,167],"these":[37],"two":[38,96],"quantities":[39,97],"more":[41,73,182],"nuanced":[42],"than":[43,83,184],"previously":[44,185],"thought.":[45],"For":[46],"example,":[47],"find":[49],"small":[53],"noise":[54],"regime,":[55],"actually":[58],"provides":[59],"an":[60,80],"upper":[61],"information.":[65,88,155],"Generally":[66],"our":[67],"results":[68,108],"show":[69],"it":[71,201],"appropriate":[74],"consider":[76],"as":[79,164],"approximation":[81,104],"rather":[82],"We":[89,156,198],"analytically":[90],"derive":[91,157],"correspondence":[93,166],"and":[98,115,122,144,172],"conditions":[100],"under":[101],"which":[102],"good.":[106],"Our":[107],"have":[109],"implications":[110],"for":[111],"theories":[114],"link":[117],"population":[120,150,169],"psychophysically":[123],"measurable":[124],"behavior.":[125],"Specifically,":[126],"they":[127],"allow":[128],"us":[129],"formulate":[131],"efficient":[133,161,219],"problem":[135],"maximizing":[137],"stimulus":[142,177],"variable":[143],"response":[146],"terms":[152],"signature":[159,180],"expressed":[163],"distribution":[174],"variable.":[178],"The":[179],"general":[183],"proposed":[186],"solutions":[187],"rely":[189],"specific":[191],"assumptions":[192],"about":[193],"tuning":[196,205],"characteristics.":[197],"can":[202],"explain":[203],"measured":[204],"characteristics":[206],"cortical":[208],"populations":[210],"do":[212],"not":[213],"agree":[214],"with":[215],"previous":[216],"models":[217],"coding.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}