{"id":"https://openalex.org/W7160405081","doi":"https://doi.org/10.48550/arxiv.2605.02989","title":"Information Theory and Statistical Learning","display_name":"Information Theory and Statistical Learning","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160405081","doi":"https://doi.org/10.48550/arxiv.2605.02989"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02989","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02989","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":null,"license_id":null,"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.2605.02989","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078716556","display_name":"Abbas El Gamal","orcid":"https://orcid.org/0000-0002-0853-0415"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gamal, Abbas El","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078716556"],"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.21490000188350677,"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"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.21490000188350677,"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/T11875","display_name":"Statistics Education and Methodologies","score":0.12319999933242798,"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/T13748","display_name":"Advanced Statistical Modeling Techniques","score":0.04230000078678131,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/preprint","display_name":"Preprint","score":0.5737000107765198},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.5098000168800354},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4553999900817871},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.4424999952316284},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.40470001101493835},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.4016999900341034},{"id":"https://openalex.org/keywords/statistical-learning-theory","display_name":"Statistical learning theory","score":0.3937999904155731},{"id":"https://openalex.org/keywords/statistical-theory","display_name":"Statistical theory","score":0.367900013923645},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.35830000042915344}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5774000287055969},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.5737000107765198},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.5098000168800354},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5045999884605408},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4553999900817871},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.4424999952316284},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.40470001101493835},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.4016999900341034},{"id":"https://openalex.org/C2779915298","wikidata":"https://www.wikidata.org/wiki/Q7604400","display_name":"Statistical learning theory","level":3,"score":0.3937999904155731},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3736000061035156},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.367900013923645},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C32254414","wikidata":"https://www.wikidata.org/wiki/Q4724364","display_name":"Algorithmic learning theory","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28439998626708984},{"id":"https://openalex.org/C2982736386","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Statistical learning","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C143095724","wikidata":"https://www.wikidata.org/wiki/Q515895","display_name":"Odds","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C2777626052","wikidata":"https://www.wikidata.org/wiki/Q516445","display_name":"Bachelor","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C180198813","wikidata":"https://www.wikidata.org/wiki/Q121182","display_name":"Information system","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C2779089604","wikidata":"https://www.wikidata.org/wiki/Q7169333","display_name":"Permission","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C92393732","wikidata":"https://www.wikidata.org/wiki/Q1790374","display_name":"Learning theory","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02989","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02989","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02989","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02989","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.5445033311843872}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,67],"manuscript":[1,68],"contains":[2],"preprint":[3],"of":[4,16,22,32,36,63,75,116,159],"a":[5,70,165],"chapter":[6,111],"under":[7],"consideration":[8],"for":[9,103],"inclusion":[10],"in":[11,56,83,119,174],"the":[12,37,61,76,89,99,114,145,152,157,160,175],"forthcoming":[13],"third":[14],"edition":[15,39],"{\\em":[17],"Cover":[18],"and":[19,52,60,72,86,127,140,151,168],"Thomas's":[20],"Elements":[21],"Information":[23],"Theory},":[24],"posted":[25],"with":[26,122],"permission":[27],"from":[28,125],"Wiley.":[29],"The":[30,110],"table":[31],"contents":[33],"EIT-3":[34],"ToC":[35],"new":[38],"can":[40],"be":[41],"found":[42],"at:":[43],"https://docs.google.com/document/d/1L-m4oQEJw1PJhoxBeMwrrBD8S_HmvzMEkPbYvS24980/edit?usp=sharing":[44],".":[45],"For":[46],"feedback,":[47],"please":[48],"contact":[49],"abbas@ee.stanford.edu":[50],"Learning":[51],"information":[53,84],"theory":[54,85],"intersect":[55],"both":[57],"model":[58,120,163],"training":[59],"characterization":[62],"fundamental":[64],"performance":[65],"limits.":[66],"provides":[69,164],"concise":[71],"accessible":[73],"treatment":[74,158],"first":[77],"intersection,":[78],"requiring":[79],"only":[80],"basic":[81],"background":[82],"statistics":[87],"at":[88],"senior":[90],"undergraduate":[91],"or":[92],"first-year":[93],"graduate":[94],"level.":[95],"End-of-chapter":[96],"exercises":[97],"make":[98],"material":[100],"well":[101,107],"suited":[102],"classroom":[104],"use":[105],"as":[106,108],"self-study.":[109],"focuses":[112],"on":[113],"role":[115],"divergence":[117],"measures":[118],"training,":[121],"examples":[123],"ranging":[124],"linear":[126],"logistic":[128],"regression":[129],"to":[130],"autoregressive":[131],"models,":[132,136],"variational":[133],"autoencoders,":[134],"diffusion":[135,162],"generative":[137,161],"adversarial":[138],"networks,":[139],"score-based":[141],"models.":[142],"It":[143],"introduces":[144],"evidence":[146],"lower":[147],"bound":[148],"(ELBO),":[149],"$f$\\!-divergences,":[150],"Fisher":[153],"divergence.":[154],"In":[155],"particular,":[156],"more":[166],"systematic":[167],"explicit":[169],"derivation":[170],"than":[171],"is":[172],"typical":[173],"literature.":[176]},"counts_by_year":[],"updated_date":"2026-05-07T06:12:12.454206","created_date":"2026-05-07T00:00:00"}