{"id":"https://openalex.org/W7220434162","doi":"https://doi.org/10.48550/arxiv.2610.03647","title":"Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models","display_name":"Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220434162","doi":"https://doi.org/10.48550/arxiv.2610.03647"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03647","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03647","pdf_url":"https://arxiv.org/pdf/2610.03647","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03647","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093666832","display_name":"Maksym Tretiakov","orcid":"https://orcid.org/0009-0007-4669-7199","observed_orcids":["https://orcid.org/0009-0007-4669-7199"]},"institutions":[{"id":"https://openalex.org/I4403386549","display_name":"Munich Center for Machine Learning","ror":"https://ror.org/02nfy3535","country_code":"DE","type":"education","lineage":["https://openalex.org/I4403386549","https://openalex.org/I62916508","https://openalex.org/I8204097"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tretiakov, Maksym","raw_affiliation_strings":["LMU Munich ,","Munich Center for Machine Learning (MCML) ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMU Munich ,","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Munich Center for Machine Learning (MCML) ,","institution_ids":["https://openalex.org/I4403386549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009767898","display_name":"Sarah Filippi","orcid":"https://orcid.org/0000-0001-8652-358X","observed_orcids":["https://orcid.org/0000-0001-8652-358X"]},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Filippi, Sarah","raw_affiliation_strings":["Imperial College London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010706885","display_name":"Vincent Fortuin","orcid":"https://orcid.org/0000-0002-0640-2671","observed_orcids":["https://orcid.org/0000-0002-0640-2671"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fortuin, Vincent","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054244566","display_name":"Ruth Misener","orcid":"https://orcid.org/0000-0001-5612-5417","observed_orcids":["https://orcid.org/0000-0001-5612-5417"]},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Misener, Ruth","raw_affiliation_strings":["Imperial College London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089206130","display_name":"Ruby Sedgwick","orcid":"https://orcid.org/0000-0001-8267-7995","observed_orcids":["https://orcid.org/0000-0001-8267-7995"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sedgwick, Ruby","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080850719","display_name":"James Odgers","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Odgers, James","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":1.0,"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":1.0,"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/T10028","display_name":"Topic Modeling","score":0.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-variational-inference","display_name":"stochastic variational inference","score":0.9599999785423279},{"id":"https://openalex.org/keywords/gaussian-process-latent-variable-model","display_name":"Gaussian process latent variable model","score":0.9940000176429749},{"id":"https://openalex.org/keywords/epistemic-uncertainty","display_name":"epistemic uncertainty","score":0.9269999861717224},{"id":"https://openalex.org/keywords/inducing-points","display_name":"inducing points","score":0.7540000081062317},{"id":"https://openalex.org/keywords/mean-field-approximation","display_name":"mean-field approximation","score":0.6809999942779541},{"id":"https://openalex.org/keywords/manifold-learning","display_name":"manifold learning","score":0.5580000281333923},{"id":"https://openalex.org/keywords/uncertainty-estimation","display_name":"uncertainty estimation","score":0.49000000953674316}],"concepts":[{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.6796000003814697},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.6359999775886536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6310999989509583},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6072999835014343},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4620000123977661},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41760000586509705},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.4129999876022339},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40059998631477356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3982999920845032},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39070001244544983},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.36579999327659607},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3449999988079071},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3386000096797943},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.3280999958515167},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C72010251","wikidata":"https://www.wikidata.org/wiki/Q5265688","display_name":"Determinantal point process","level":4,"score":0.26809999346733093},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.265500009059906},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03647","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03647","pdf_url":"https://arxiv.org/pdf/2610.03647","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03647","doi":"https://doi.org/10.48550/arxiv.2610.03647","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03647","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03647","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03647","pdf_url":"https://arxiv.org/pdf/2610.03647","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1665795692","display_name":"Transforming synthetic drug manufacturing: novel processes, methods and tools","funder_award_id":"EP/T005556/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3408814581","display_name":null,"funder_award_id":"EP/T005556","funder_id":"https://openalex.org/F4320307758","funder_display_name":"Eli Lilly and Company"},{"id":"https://openalex.org/G3457321631","display_name":null,"funder_award_id":"EP/T005556/1","funder_id":"https://openalex.org/F4320307758","funder_display_name":"Eli Lilly and Company"},{"id":"https://openalex.org/G8383953059","display_name":null,"funder_award_id":"EP/T005556","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320307758","display_name":"Eli Lilly and Company","ror":"https://ror.org/01qat3289"},{"id":"https://openalex.org/F4320320283","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220434162.pdf","grobid_xml":"https://content.openalex.org/works/W7220434162.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1986944049","https://openalex.org/W2125027820","https://openalex.org/W2225156818","https://openalex.org/W2750384547","https://openalex.org/W4393929107","https://openalex.org/W4402427090","https://openalex.org/W4403450538","https://openalex.org/W4407570103"],"related_works":["https://openalex.org/W2765737382","https://openalex.org/W1777124189","https://openalex.org/W7096979683","https://openalex.org/W1895281781","https://openalex.org/W4403747075","https://openalex.org/W2278171434","https://openalex.org/W3026126175","https://openalex.org/W4221149770","https://openalex.org/W3033768482","https://openalex.org/W7097562369"],"abstract_inverted_index":{"Many":[0],"machine":[1],"learning":[2],"methods":[3,20],"aim":[4],"to":[5,98,107,130],"approximate":[6],"the":[7,12,26,39,53,60,63,66,75,80,85,100,104,112,115,131,136],"lower-dimensional":[8],"manifold":[9],"on":[10,111,135],"which":[11,46],"data":[13,137],"lives.":[14],"A":[15],"desirable":[16],"feature":[17],"of":[18,29,59,62,68,114,133],"such":[19],"is":[21,38,72],"that":[22,35,120],"they":[23],"should":[24],"capture":[25],"epistemic":[27],"uncertainty":[28,61,70],"this":[30,37,69,89,121],"learned":[31],"manifold.":[32,64,138],"One":[33],"model":[34],"achieves":[36],"Gaussian":[40,48],"Process":[41,49],"Latent":[42],"Variable":[43],"Model,":[44],"in":[45],"a":[47],"(GP)":[50],"mapping":[51],"from":[52],"latent":[54,86,105],"space":[55,106],"provides":[56],"an":[57],"estimate":[58],"However,":[65],"effectiveness":[67],"estimation":[71],"limited":[73],"by":[74],"mean-field":[76],"variational":[77,101,124],"approximation":[78],"between":[79],"GP":[81],"inducing":[82,116],"points":[83,134],"and":[84],"variables.":[87],"In":[88],"work,":[90],"we":[91],"apply":[92],"Amortized":[93],"Structured":[94],"Stochastic":[95],"Variational":[96],"Inference":[97],"allow":[99],"posterior":[102,125],"for":[103],"be":[108],"conditionally":[109],"dependent":[110],"value":[113],"points.":[117],"We":[118],"demonstrate":[119],"more":[122],"flexible":[123],"improves":[126],"several":[127],"metrics":[128],"relating":[129],"reconstruction":[132]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}