{"id":"https://openalex.org/W4400723054","doi":"https://doi.org/10.1007/s10208-024-09663-w","title":"Regularized Stein Variational Gradient Flow","display_name":"Regularized Stein Variational Gradient Flow","publication_year":2024,"publication_date":"2024-07-17","ids":{"openalex":"https://openalex.org/W4400723054","doi":"https://doi.org/10.1007/s10208-024-09663-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-024-09663-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09663-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09663-w.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09663-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101610257","display_name":"Ye He","orcid":"https://orcid.org/0000-0003-4686-8449"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ye He","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332, USA"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014500490","display_name":"Krishnakumar Balasubramanian","orcid":"https://orcid.org/0000-0003-1472-9559"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Krishnakumar Balasubramanian","raw_affiliation_strings":["Department of Statistics, University of California, Davis, 399 Crocker Lane, One Shields Avenue, Davis, CA, 95616, USA"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of California, Davis, 399 Crocker Lane, One Shields Avenue, Davis, CA, 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109582233","display_name":"Bharath K. Sriperumbudur","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bharath K. Sriperumbudur","raw_affiliation_strings":["Department of Statistics, Pennsylvania State University, 314, Thomas Building, University Park, PA, 16802, USA"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Pennsylvania State University, 314, Thomas Building, University Park, PA, 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061472917","display_name":"Jianfeng Lu","orcid":"https://orcid.org/0000-0001-6255-5165"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianfeng Lu","raw_affiliation_strings":["Mathematics Department, Duke University, Box 90320, 120 Science Dr., Durham, NC, 27708-0320, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Duke University, Box 90320, 120 Science Dr., Durham, NC, 27708-0320, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014500490"],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.0363,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.72711447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"25","issue":"4","first_page":"1199","last_page":"1257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.8659443259239197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7854596376419067},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.702568531036377},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6893133521080017},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6183193922042847},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.565776526927948},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5567003488540649},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5443896055221558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5079076886177063},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4506790339946747},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.43523353338241577},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2574484944343567},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1547812521457672},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10859555006027222},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0897759199142456}],"concepts":[{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.8659443259239197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7854596376419067},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.702568531036377},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6893133521080017},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6183193922042847},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.565776526927948},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5567003488540649},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5443896055221558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5079076886177063},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4506790339946747},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.43523353338241577},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2574484944343567},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1547812521457672},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10859555006027222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0897759199142456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-024-09663-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09663-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09663-w.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10208-024-09663-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09663-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09663-w.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4400723054.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W187557541","https://openalex.org/W423603040","https://openalex.org/W1489867037","https://openalex.org/W1522579744","https://openalex.org/W1565176583","https://openalex.org/W1992957154","https://openalex.org/W2000200506","https://openalex.org/W2071048859","https://openalex.org/W2074043571","https://openalex.org/W2093943787","https://openalex.org/W2124331852","https://openalex.org/W2275636546","https://openalex.org/W2398886555","https://openalex.org/W2441221256","https://openalex.org/W2494401598","https://openalex.org/W2511837229","https://openalex.org/W2519388618","https://openalex.org/W2565482624","https://openalex.org/W2760093735","https://openalex.org/W2787957431","https://openalex.org/W2898856356","https://openalex.org/W2948375734","https://openalex.org/W2962937842","https://openalex.org/W2963134136","https://openalex.org/W2963172141","https://openalex.org/W2964015695","https://openalex.org/W2970698058","https://openalex.org/W2973214398","https://openalex.org/W2980329363","https://openalex.org/W2990020588","https://openalex.org/W3033450417","https://openalex.org/W3035094823","https://openalex.org/W3036693463","https://openalex.org/W3088538132","https://openalex.org/W3134081794","https://openalex.org/W4212774754","https://openalex.org/W4221151467","https://openalex.org/W4221165920","https://openalex.org/W4225861965","https://openalex.org/W4245558064","https://openalex.org/W4254086930","https://openalex.org/W4287124663","https://openalex.org/W4378508629"],"related_works":["https://openalex.org/W4287028882","https://openalex.org/W2891466145","https://openalex.org/W4309201680","https://openalex.org/W4387963920","https://openalex.org/W2610139381","https://openalex.org/W2507690919","https://openalex.org/W4287077847","https://openalex.org/W4381797995","https://openalex.org/W4310430694","https://openalex.org/W263682811"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"stein":[2],"variational":[3],"gradient":[4,22,43,72],"descent":[5],"(SVGD)":[6],"algorithm":[7,28],"is":[8],"a":[9,16,37],"deterministic":[10],"particle":[11],"method":[12],"for":[13],"sampling.":[14],"However,":[15],"mean-field":[17],"analysis":[18],"reveals":[19],"that":[20],"the":[21,26,30,41,47,55,64,70,80,102,110,115],"flow":[23,44],"corresponding":[24,45],"to":[25,40,46,91],"SVGD":[27],"(i.e.,":[29],"Stein":[31,57,65,82],"Variational":[32,58,66,83],"Gradient":[33,59,67,84],"Flow)":[34],"only":[35],"provides":[36],"constant-order":[38],"approximation":[39],"Wasserstein":[42,71],"KL-divergence":[48],"minimization.":[49],"In":[50],"this":[51],"work,":[52],"we":[53],"propose":[54],"Regularized":[56,81],"Flow,":[60],"which":[61],"interpolates":[62],"between":[63],"Flow":[68,85],"and":[69,94,99],"flow.":[73],"We":[74,104],"establish":[75],"various":[76],"theoretical":[77],"properties":[78],"of":[79,96,101,109],"(and":[86],"its":[87],"time-discretization)":[88],"including":[89],"convergence":[90],"equilibrium,":[92],"existence":[93],"uniqueness":[95],"weak":[97],"solutions,":[98],"stability":[100],"solutions.":[103],"provide":[105],"preliminary":[106],"numerical":[107],"evidence":[108],"improved":[111],"performance":[112],"offered":[113],"by":[114],"regularization.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}