<> <http://www.w3.org/2000/01/rdf-schema#comment> "The repository administrator has not yet configured an RDF license."^^<http://www.w3.org/2001/XMLSchema#string> . <> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10166658> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/dc/terms/title> "A Non-Asymptotic Analysis for\r\nStein Variational Gradient Descent"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/abstract> "We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution π ∠e\r\n−V\r\non R\r\nd. In the population limit, SVGD performs gradient descent in the space\r\nof probability distributions on the KL divergence with respect to π, where the\r\ngradient is smoothed through a kernel integral operator. In this paper, we provide a\r\nnovel finite time analysis for the SVGD algorithm. We provide a descent lemma\r\nestablishing that the algorithm decreases the objective at each iteration, and rates\r\nof convergence for the averaged Stein Fisher divergence (also referred to as Kernel\r\nStein Discrepancy). We also provide a convergence result of the finite particle\r\nsystem corresponding to the practical implementation of SVGD to its population\r\nversion."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/dc/terms/date> "2020-12-06" . <https://discovery.ucl.ac.uk/id/document/1525892> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/volume> "2020" . <https://discovery.ucl.ac.uk/id/org/ext-5f6fd9fe3545af920225f7c1630b4c59> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Organization> . <https://discovery.ucl.ac.uk/id/org/ext-5f6fd9fe3545af920225f7c1630b4c59> <http://xmlns.com/foaf/0.1/name> "Neural Information Processing Systems Conference"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/dc/terms/publisher> <https://discovery.ucl.ac.uk/id/org/ext-5f6fd9fe3545af920225f7c1630b4c59> . <https://discovery.ucl.ac.uk/id/publication/ext-10495258> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Collection> . <https://discovery.ucl.ac.uk/id/publication/ext-10495258> <http://xmlns.com/foaf/0.1/name> "Advances in Neural Information Processing Systems"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/publication/ext-10495258> . <https://discovery.ucl.ac.uk/id/publication/ext-10495258> <http://www.w3.org/2002/07/owl#sameAs> <urn:issn:10495258> . <https://discovery.ucl.ac.uk/id/publication/ext-10495258> <http://purl.org/ontology/bibo/issn> "10495258" . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/status> <http://purl.org/ontology/bibo/status/published> . <https://discovery.ucl.ac.uk/id/eprint/10166658> 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<http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-d0b10be6e9daa2b2847a1840132de1f8> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#authors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-d0b10be6e9daa2b2847a1840132de1f8> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-39f659e9f29a3e8c56e06407118cb048> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#authors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_4> <https://discovery.ucl.ac.uk/id/person/ext-39f659e9f29a3e8c56e06407118cb048> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-e30299ae01ced2a9010408c496378ddb> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#authors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_5> <https://discovery.ucl.ac.uk/id/person/ext-e30299ae01ced2a9010408c496378ddb> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-a0f2971a04efaf42a0c7b084f073b0c1> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-a0f2971a04efaf42a0c7b084f073b0c1> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-6a603ff85b5278365e3f38085046b1fa> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-6a603ff85b5278365e3f38085046b1fa> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-a73ad07dc4b2947b070ea398510cd17a> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-a73ad07dc4b2947b070ea398510cd17a> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-59fc3b5bbb0ffb214c7ca7a7d1286f89> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_4> <https://discovery.ucl.ac.uk/id/person/ext-59fc3b5bbb0ffb214c7ca7a7d1286f89> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-b0aeb2e756a17881a381c49f8cfd92b7> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> . <https://discovery.ucl.ac.uk/id/eprint/10166658#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_5> <https://discovery.ucl.ac.uk/id/person/ext-b0aeb2e756a17881a381c49f8cfd92b7> . <https://discovery.ucl.ac.uk/id/person/ext-39f659e9f29a3e8c56e06407118cb048> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-39f659e9f29a3e8c56e06407118cb048> <http://xmlns.com/foaf/0.1/givenName> "G"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-39f659e9f29a3e8c56e06407118cb048> <http://xmlns.com/foaf/0.1/familyName> "Luise"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-39f659e9f29a3e8c56e06407118cb048> <http://xmlns.com/foaf/0.1/name> "G Luise"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-d0b10be6e9daa2b2847a1840132de1f8> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-d0b10be6e9daa2b2847a1840132de1f8> <http://xmlns.com/foaf/0.1/givenName> "M"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-d0b10be6e9daa2b2847a1840132de1f8> <http://xmlns.com/foaf/0.1/familyName> "Arbel"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-d0b10be6e9daa2b2847a1840132de1f8> <http://xmlns.com/foaf/0.1/name> "M Arbel"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-59fc3b5bbb0ffb214c7ca7a7d1286f89> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-59fc3b5bbb0ffb214c7ca7a7d1286f89> <http://xmlns.com/foaf/0.1/givenName> "M.F."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-59fc3b5bbb0ffb214c7ca7a7d1286f89> <http://xmlns.com/foaf/0.1/familyName> "Balcan"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-59fc3b5bbb0ffb214c7ca7a7d1286f89> <http://xmlns.com/foaf/0.1/name> "M.F. Balcan"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-b0aeb2e756a17881a381c49f8cfd92b7> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-b0aeb2e756a17881a381c49f8cfd92b7> <http://xmlns.com/foaf/0.1/givenName> "H."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-b0aeb2e756a17881a381c49f8cfd92b7> <http://xmlns.com/foaf/0.1/familyName> "Lin"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-b0aeb2e756a17881a381c49f8cfd92b7> <http://xmlns.com/foaf/0.1/name> "H. Lin"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-cb0f5360f8511274df10088ffde32113> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-cb0f5360f8511274df10088ffde32113> <http://xmlns.com/foaf/0.1/givenName> "A"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-cb0f5360f8511274df10088ffde32113> <http://xmlns.com/foaf/0.1/familyName> "Salim"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-cb0f5360f8511274df10088ffde32113> <http://xmlns.com/foaf/0.1/name> "A Salim"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-6a603ff85b5278365e3f38085046b1fa> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-6a603ff85b5278365e3f38085046b1fa> <http://xmlns.com/foaf/0.1/givenName> "M."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-6a603ff85b5278365e3f38085046b1fa> <http://xmlns.com/foaf/0.1/familyName> "Ranzato"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-6a603ff85b5278365e3f38085046b1fa> <http://xmlns.com/foaf/0.1/name> "M. Ranzato"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-e30299ae01ced2a9010408c496378ddb> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-e30299ae01ced2a9010408c496378ddb> <http://xmlns.com/foaf/0.1/givenName> "A"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-e30299ae01ced2a9010408c496378ddb> <http://xmlns.com/foaf/0.1/familyName> "Gretton"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-e30299ae01ced2a9010408c496378ddb> <http://xmlns.com/foaf/0.1/name> "A Gretton"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-125a9d5d815332a8fa0a24419196859b> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-125a9d5d815332a8fa0a24419196859b> <http://xmlns.com/foaf/0.1/givenName> "A"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-125a9d5d815332a8fa0a24419196859b> <http://xmlns.com/foaf/0.1/familyName> "Korba"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-125a9d5d815332a8fa0a24419196859b> <http://xmlns.com/foaf/0.1/name> "A Korba"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-a0f2971a04efaf42a0c7b084f073b0c1> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-a0f2971a04efaf42a0c7b084f073b0c1> <http://xmlns.com/foaf/0.1/givenName> "H."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-a0f2971a04efaf42a0c7b084f073b0c1> <http://xmlns.com/foaf/0.1/familyName> "Larochelle"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-a0f2971a04efaf42a0c7b084f073b0c1> <http://xmlns.com/foaf/0.1/name> "H. Larochelle"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-a73ad07dc4b2947b070ea398510cd17a> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-a73ad07dc4b2947b070ea398510cd17a> <http://xmlns.com/foaf/0.1/givenName> "R."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-a73ad07dc4b2947b070ea398510cd17a> <http://xmlns.com/foaf/0.1/familyName> "Hadsell"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-a73ad07dc4b2947b070ea398510cd17a> <http://xmlns.com/foaf/0.1/name> "R. Hadsell"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://purl.org/ontology/bibo/presentedAt> <https://discovery.ucl.ac.uk/id/event/ext-352cf980b20aa220afa069b29dea0687> . <https://discovery.ucl.ac.uk/id/event/ext-352cf980b20aa220afa069b29dea0687> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Conference> . <https://discovery.ucl.ac.uk/id/event/ext-352cf980b20aa220afa069b29dea0687> <http://purl.org/dc/terms/title> "NIPS'20: 34th International Conference on Neural Information Processing Systems"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10166658> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/EPrint> . <https://discovery.ucl.ac.uk/id/eprint/10166658> 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