{"id":"https://openalex.org/W7128736826","doi":"https://doi.org/10.48550/arxiv.2602.10602","title":"Learning Mixture Density via Natural Gradient Expectation Maximization","display_name":"Learning Mixture Density via Natural Gradient Expectation Maximization","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128736826","doi":"https://doi.org/10.48550/arxiv.2602.10602"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.10602","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043053100","display_name":"Yutao Chen","orcid":"https://orcid.org/0000-0001-9442-6368"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Yutao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030149528","display_name":"Jasmine Bayrooti","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bayrooti, Jasmine","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074062972","display_name":"Steven Morad","orcid":"https://orcid.org/0000-0002-8413-2953"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Morad, Steven","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043053100"],"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.47940000891685486,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.47940000891685486,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.12929999828338623,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.12639999389648438,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mixture-model","display_name":"Mixture model","score":0.6847000122070312},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6697999835014343},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.6434999704360962},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.6341999769210815},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5192000269889832},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.5162000060081482},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5091999769210815},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.42809998989105225},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.390500009059906}],"concepts":[{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.6847000122070312},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6697999835014343},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.6434999704360962},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.6341999769210815},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5192000269889832},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.5162000060081482},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4657999873161316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.460999995470047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4381999969482422},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.42809998989105225},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.390500009059906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.376800000667572},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.376800000667572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3700000047683716},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3467999994754791},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C56672385","wikidata":"https://www.wikidata.org/wiki/Q17157111","display_name":"Mixture distribution","level":3,"score":0.31220000982284546},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.30570000410079956},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.250900000333786},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.10602","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.10602","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.10602","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.10602","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Mixture":[0],"density":[1,46,57],"networks":[2,5,47,58],"are":[3],"neural":[4],"that":[6,96],"produce":[7],"Gaussian":[8],"mixtures":[9],"to":[10,76,85,101,113],"represent":[11],"continuous":[12],"multimodal":[13],"conditional":[14],"densities.":[15],"Standard":[16],"training":[17],"procedures":[18],"involve":[19],"maximum":[20],"likelihood":[21],"estimation":[22],"using":[23],"the":[24,42,87],"negative":[25],"log-likelihood":[26],"(NLL)":[27],"objective,":[28],"which":[29,71],"suffers":[30],"from":[31],"slow":[32],"convergence":[33,104],"and":[34,63,110],"mode":[35],"collapse.":[36],"In":[37],"this":[38],"work,":[39],"we":[40,54],"improve":[41],"optimization":[43],"of":[44],"mixture":[45,56],"by":[48],"integrating":[49],"their":[50],"information":[51],"geometry.":[52],"Specifically,":[53],"interpret":[55],"as":[59],"deep":[60],"latent-variable":[61],"models":[62],"analyze":[64],"them":[65],"through":[66],"an":[67],"expectation":[68,90],"maximization":[69,91],"framework,":[70],"reveals":[72],"surprising":[73],"theoretical":[74],"connections":[75,84],"natural":[77,88],"gradient":[78,89],"descent.":[79],"We":[80,94],"then":[81],"exploit":[82],"such":[83],"derive":[86],"(nGEM)":[92],"objective.":[93],"show":[95],"empirically":[97],"nGEM":[98],"achieves":[99],"up":[100],"10$\\times$":[102],"faster":[103],"while":[105],"adding":[106],"almost":[107],"zerocomputational":[108],"overhead,":[109],"scales":[111],"well":[112],"high-dimensional":[114],"data":[115],"where":[116],"NLL":[117],"otherwise":[118],"fails.":[119]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-13T00:00:00"}