{"id":"https://openalex.org/W2528005577","doi":"https://doi.org/10.1007/s10208-016-9331-y","title":"An Interpolating Distance Between Optimal Transport and Fisher\u2013Rao Metrics","display_name":"An Interpolating Distance Between Optimal Transport and Fisher\u2013Rao Metrics","publication_year":2016,"publication_date":"2016-10-03","ids":{"openalex":"https://openalex.org/W2528005577","doi":"https://doi.org/10.1007/s10208-016-9331-y","mag":"2528005577"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-016-9331-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-016-9331-y","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010177550","display_name":"L\u00e9na\u00efc Chizat","orcid":"https://orcid.org/0000-0002-6553-1211"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L\u00e9na\u00efc Chizat","raw_affiliation_strings":["Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I171048554","https://openalex.org/I56435720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058651667","display_name":"Gabriel Peyr\u00e9","orcid":"https://orcid.org/0000-0002-4477-0387"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gabriel Peyr\u00e9","raw_affiliation_strings":["Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I171048554","https://openalex.org/I56435720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059838227","display_name":"Bernhard Schmitzer","orcid":"https://orcid.org/0000-0002-6146-8833"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bernhard Schmitzer","raw_affiliation_strings":["Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I171048554","https://openalex.org/I56435720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110944327","display_name":"Fran\u00e7ois\u2010Xavier Vialard","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois-Xavier Vialard","raw_affiliation_strings":["Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Project team Mokaplan, CEREMADE, CNRS, INRIA, Universit\u00e9 Paris-Dauphine, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I171048554","https://openalex.org/I56435720"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110944327"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I171048554","https://openalex.org/I56435720"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":22.2084,"has_fulltext":false,"cited_by_count":170,"citation_normalized_percentile":{"value":0.9980483,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"18","issue":"1","first_page":"1","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9993000030517578,"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":0.9993000030517578,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9918000102043152,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.986299991607666,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.8656711578369141},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8251344561576843},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7311112880706787},{"id":"https://openalex.org/keywords/wasserstein-metric","display_name":"Wasserstein metric","score":0.5910106897354126},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5393173098564148},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5367751121520996},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5345847606658936},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.505287230014801},{"id":"https://openalex.org/keywords/steins-method","display_name":"Stein's method","score":0.501612663269043},{"id":"https://openalex.org/keywords/hellinger-distance","display_name":"Hellinger distance","score":0.46219804883003235},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4141216576099396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41359373927116394},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.3970465362071991},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.22732692956924438},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.2138136923313141},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1654393970966339},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10140693187713623}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8656711578369141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8251344561576843},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7311112880706787},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.5910106897354126},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5393173098564148},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5367751121520996},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5345847606658936},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.505287230014801},{"id":"https://openalex.org/C198496030","wikidata":"https://www.wikidata.org/wiki/Q7606740","display_name":"Stein's method","level":5,"score":0.501612663269043},{"id":"https://openalex.org/C153024298","wikidata":"https://www.wikidata.org/wiki/Q3030678","display_name":"Hellinger distance","level":2,"score":0.46219804883003235},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4141216576099396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41359373927116394},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.3970465362071991},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.22732692956924438},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2138136923313141},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1654393970966339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10140693187713623},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-016-9331-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-016-9331-y","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W158030646","https://openalex.org/W1479979375","https://openalex.org/W1522579744","https://openalex.org/W1538609674","https://openalex.org/W1544168072","https://openalex.org/W1585160083","https://openalex.org/W1946620893","https://openalex.org/W1979610031","https://openalex.org/W1985506636","https://openalex.org/W1995453118","https://openalex.org/W2013176880","https://openalex.org/W2020282736","https://openalex.org/W2028852533","https://openalex.org/W2048435560","https://openalex.org/W2052424080","https://openalex.org/W2064090547","https://openalex.org/W2074745044","https://openalex.org/W2092793871","https://openalex.org/W2100630492","https://openalex.org/W2123457441","https://openalex.org/W2142280715","https://openalex.org/W2145859152","https://openalex.org/W2145936352","https://openalex.org/W2158458531","https://openalex.org/W2168637982","https://openalex.org/W2170167891","https://openalex.org/W2264170307","https://openalex.org/W2885749508","https://openalex.org/W2907535527","https://openalex.org/W2951387855","https://openalex.org/W2962701695","https://openalex.org/W3098034875","https://openalex.org/W3101978293","https://openalex.org/W4233216084"],"related_works":["https://openalex.org/W1741548419","https://openalex.org/W2952213070","https://openalex.org/W1586565821","https://openalex.org/W2172478671","https://openalex.org/W3202184724","https://openalex.org/W2528005577","https://openalex.org/W4385155821","https://openalex.org/W2997064483","https://openalex.org/W1138777372","https://openalex.org/W4378709708"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
