{"id":"https://openalex.org/W7109060896","doi":"https://doi.org/10.48550/arxiv.2512.04747","title":"A Tutorial on Regression Analysis: From Linear Models to Deep Learning -- Lecture Notes on Artificial Intelligence","display_name":"A Tutorial on Regression Analysis: From Linear Models to Deep Learning -- Lecture Notes on Artificial Intelligence","publication_year":2025,"publication_date":"2025-12-04","ids":{"openalex":"https://openalex.org/W7109060896","doi":"https://doi.org/10.48550/arxiv.2512.04747"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.04747","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.04747","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.04747","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Wang, Jingyuan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jingyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Ji, Jiahao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ji, Jiahao","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":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/T11875","display_name":"Statistics Education and Methodologies","score":0.10100000351667404,"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/T11875","display_name":"Statistics Education and Methodologies","score":0.10100000351667404,"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/T13398","display_name":"Data Analysis with R","score":0.04479999840259552,"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/T13748","display_name":"Advanced Statistical Modeling Techniques","score":0.04410000145435333,"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/multinomial-logistic-regression","display_name":"Multinomial logistic regression","score":0.5831999778747559},{"id":"https://openalex.org/keywords/polynomial-regression","display_name":"Polynomial regression","score":0.5684000253677368},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.48890000581741333},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.4426000118255615},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"Logistic regression","score":0.41990000009536743},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.4187000095844269},{"id":"https://openalex.org/keywords/bridging","display_name":"Bridging (networking)","score":0.41609999537467957},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.3982999920845032}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.7002000212669373},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.638700008392334},{"id":"https://openalex.org/C117568660","wikidata":"https://www.wikidata.org/wiki/Q1650843","display_name":"Multinomial logistic regression","level":2,"score":0.5831999778747559},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.5684000253677368},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.546999990940094},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.48890000581741333},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.41990000009536743},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C32224588","wikidata":"https://www.wikidata.org/wiki/Q7250175","display_name":"Proper linear model","level":4,"score":0.33719998598098755},{"id":"https://openalex.org/C176222170","wikidata":"https://www.wikidata.org/wiki/Q5157340","display_name":"Computational statistics","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C157170001","wikidata":"https://www.wikidata.org/wiki/Q4781507","display_name":"Applications of artificial intelligence","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.04747","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.04747","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2512.04747","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.04747","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":"Preprint"},"sustainable_development_goals":[{"score":0.4651399850845337,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"article":[1],"serves":[2],"as":[3,120,122,126],"the":[4,10,16,74,141,160],"regression":[5,62,83,149],"analysis":[6,63],"lecture":[7,70,178],"notes":[8,71,179],"in":[9,47,194],"Intelligent":[11],"Computing":[12],"course":[13],"cluster":[14],"(including":[15],"courses":[17,46],"of":[18,61,82],"Artificial":[19],"Intelligence,":[20],"Data":[21],"Mining,":[22],"Machine":[23],"Learning,":[24],"and":[25,51,58,79,99,117,128,137,153,165,173,188],"Pattern":[26],"Recognition).":[27],"It":[28],"aims":[29],"to":[30,37,181],"provide":[31],"students":[32,144,183],"--":[33,54],"who":[34],"are":[35,151],"assumed":[36],"possess":[38],"only":[39,147],"basic":[40],"university-level":[41],"mathematics":[42],"(i.e.,":[43],"with":[44,55,184],"prerequisite":[45],"calculus,":[48],"linear":[49,86],"algebra,":[50],"probability":[52],"theory)":[53],"a":[56,185],"comprehensive":[57],"self-contained":[59],"understanding":[60],"without":[64],"requiring":[65],"any":[66],"additional":[67],"references.":[68],"The":[69],"systematically":[72],"introduce":[73],"fundamental":[75],"concepts,":[76],"modeling":[77,172],"components,":[78],"theoretical":[80],"foundations":[81],"analysis,":[84],"covering":[85],"regression,":[87,89,92,94],"logistic":[88,91],"multinomial":[90],"polynomial":[93],"basis-function":[95],"models,":[96],"kernel-based":[97],"methods,":[98],"neural-network-based":[100],"nonlinear":[101],"regression.":[102,130],"Core":[103],"methodological":[104],"topics":[105],"include":[106],"loss-function":[107],"design,":[108],"parameter-estimation":[109],"principles,":[110],"ordinary":[111],"least":[112],"squares,":[113],"gradient-based":[114],"optimization":[115],"algorithms":[116],"their":[118],"variants,":[119],"well":[121],"regularization":[123],"techniques":[124],"such":[125],"Ridge":[127],"LASSO":[129],"Through":[131],"detailed":[132],"mathematical":[133],"derivations,":[134],"illustrative":[135],"examples,":[136],"intuitive":[138],"visual":[139],"explanations,":[140],"materials":[142],"help":[143],"understand":[145],"not":[146],"how":[148,157],"models":[150],"constructed":[152],"optimized,":[154],"but":[155],"also":[156],"they":[158],"reveal":[159],"underlying":[161],"relationships":[162],"between":[163],"features":[164],"response":[166],"variables.":[167],"By":[168],"bridging":[169],"classical":[170],"statistical":[171],"modern":[174],"machine-learning":[175],"practice,":[176],"these":[177],"aim":[180],"equip":[182],"solid":[186],"conceptual":[187],"technical":[189],"foundation":[190],"for":[191],"further":[192],"study":[193],"advanced":[195],"artificial":[196],"intelligence":[197],"models.":[198]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-12-06T00:00:00"}