<> <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/10192390> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/title> "Comparing Comparators in Generalization Bounds"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/abstract> "We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training loss and the population loss. The bounds hold under the assumption that the cumulant-generating function (CGF) of the comparator is upper-bounded by the corresponding CGF within a family of bounding distributions. We show that the tightest possible bound is obtained with the comparator being the convex conjugate of the CGF of the bounding distribution, also known as the Cramér function. This conclusion applies more broadly to generalization bounds with a similar structure. This confirms the near-optimality of known bounds for bounded and sub-Gaussian losses and leads to novel bounds under other bounding distributions."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/date> "2024" .
<https://discovery.ucl.ac.uk/id/document/1744282> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/volume> "238" .
<https://discovery.ucl.ac.uk/id/org/ext-4c9a5a6ca815397a052ac267d87541ef> <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-4c9a5a6ca815397a052ac267d87541ef> <http://xmlns.com/foaf/0.1/name> "PMLR (Proceedings of Machine Learning Research)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/publisher> <https://discovery.ucl.ac.uk/id/org/ext-4c9a5a6ca815397a052ac267d87541ef> .
<https://discovery.ucl.ac.uk/id/publication/ext-54ec8a6920fab3cfa718a743c7a4e4ac> <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-54ec8a6920fab3cfa718a743c7a4e4ac> <http://xmlns.com/foaf/0.1/name> "AISTATS"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/publication/ext-54ec8a6920fab3cfa718a743c7a4e4ac> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/status> <http://purl.org/ontology/bibo/status/published> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-8e5c8cf4bf68c0f39f2d63a2b7e8c7c4> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10192390#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10192390#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-8e5c8cf4bf68c0f39f2d63a2b7e8c7c4> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-9b026aba957c56a3836200b140fa8e04> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10192390#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10192390#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-9b026aba957c56a3836200b140fa8e04> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-2416203368a1d5321bc711e37399f28a> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10192390#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10192390#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-2416203368a1d5321bc711e37399f28a> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-bdd41e83996d02519e88b22ee937e689> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10192390#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10192390#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-bdd41e83996d02519e88b22ee937e689> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-b908c3b13133944295001f0a1abada19> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10192390#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10192390#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-b908c3b13133944295001f0a1abada19> .
<https://discovery.ucl.ac.uk/id/person/ext-9b026aba957c56a3836200b140fa8e04> <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-9b026aba957c56a3836200b140fa8e04> <http://xmlns.com/foaf/0.1/givenName> "Benjamin"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-9b026aba957c56a3836200b140fa8e04> <http://xmlns.com/foaf/0.1/familyName> "Guedj"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-9b026aba957c56a3836200b140fa8e04> <http://xmlns.com/foaf/0.1/name> "Benjamin Guedj"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-bdd41e83996d02519e88b22ee937e689> <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-bdd41e83996d02519e88b22ee937e689> <http://xmlns.com/foaf/0.1/givenName> "Stephan"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-bdd41e83996d02519e88b22ee937e689> <http://xmlns.com/foaf/0.1/familyName> "Mandt"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-bdd41e83996d02519e88b22ee937e689> <http://xmlns.com/foaf/0.1/name> "Stephan Mandt"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-b908c3b13133944295001f0a1abada19> <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-b908c3b13133944295001f0a1abada19> <http://xmlns.com/foaf/0.1/givenName> "Yingzhen"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-b908c3b13133944295001f0a1abada19> <http://xmlns.com/foaf/0.1/familyName> "Li"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-b908c3b13133944295001f0a1abada19> <http://xmlns.com/foaf/0.1/name> "Yingzhen Li"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-8e5c8cf4bf68c0f39f2d63a2b7e8c7c4> <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-8e5c8cf4bf68c0f39f2d63a2b7e8c7c4> <http://xmlns.com/foaf/0.1/givenName> "Fredrik"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-8e5c8cf4bf68c0f39f2d63a2b7e8c7c4> <http://xmlns.com/foaf/0.1/familyName> "Hellström"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-8e5c8cf4bf68c0f39f2d63a2b7e8c7c4> <http://xmlns.com/foaf/0.1/name> "Fredrik Hellström"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-2416203368a1d5321bc711e37399f28a> <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-2416203368a1d5321bc711e37399f28a> <http://xmlns.com/foaf/0.1/givenName> "Sanjoy"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-2416203368a1d5321bc711e37399f28a> <http://xmlns.com/foaf/0.1/familyName> "Dasgupta"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-2416203368a1d5321bc711e37399f28a> <http://xmlns.com/foaf/0.1/name> "Sanjoy Dasgupta"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/ontology/bibo/presentedAt> <https://discovery.ucl.ac.uk/id/event/ext-dc73201ec7f15ad2c3b4e4e5f0616e9a> .
<https://discovery.ucl.ac.uk/id/event/ext-dc73201ec7f15ad2c3b4e4e5f0616e9a> <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-dc73201ec7f15ad2c3b4e4e5f0616e9a> <http://purl.org/dc/terms/title> "The 27th International Conference on Artificial Intelligence and Statistics"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/EPrint> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/ProceedingsSectionEPrint> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/repository> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744282> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1744282> <http://www.w3.org/2000/01/rdf-schema#label> "Comparing Comparators in Generalization Bounds (PDF)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://purl.org/dc/elements/1.1/hasVersion> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasPublished> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744282> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10192390/1/hellstrom24a.pdf> .
<https://discovery.ucl.ac.uk/id/document/1744282> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10192390/1/hellstrom24a.pdf> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/1/hellstrom24a.pdf> <http://www.w3.org/2000/01/rdf-schema#label> "hellstrom24a.pdf"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1744283> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://www.w3.org/2000/01/rdf-schema#label> "Comparing Comparators in Generalization Bounds (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://eprints.org/relation/isIndexCodesVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10192390/2/indexcodes.txt> .
<https://discovery.ucl.ac.uk/id/document/1744283> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10192390/2/indexcodes.txt> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/2/indexcodes.txt> <http://www.w3.org/2000/01/rdf-schema#label> "indexcodes.txt"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1744284> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://www.w3.org/2000/01/rdf-schema#label> "Comparing Comparators in Generalization Bounds (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://eprints.org/relation/islightboxThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10192390/3/lightbox.jpg> .
<https://discovery.ucl.ac.uk/id/document/1744284> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10192390/3/lightbox.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/3/lightbox.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "lightbox.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1744285> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://www.w3.org/2000/01/rdf-schema#label> "Comparing Comparators in Generalization Bounds (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://eprints.org/relation/ispreviewThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10192390/4/preview.jpg> .
<https://discovery.ucl.ac.uk/id/document/1744285> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10192390/4/preview.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/4/preview.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "preview.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1744286> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://www.w3.org/2000/01/rdf-schema#label> "Comparing Comparators in Generalization Bounds (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://eprints.org/relation/ismediumThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10192390/5/medium.jpg> .
<https://discovery.ucl.ac.uk/id/document/1744286> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10192390/5/medium.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/5/medium.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "medium.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1744287> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://www.w3.org/2000/01/rdf-schema#label> "Comparing Comparators in Generalization Bounds (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://eprints.org/relation/issmallThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1744282> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10192390/6/small.jpg> .
<https://discovery.ucl.ac.uk/id/document/1744287> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10192390/6/small.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/6/small.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "small.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10192390> <http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://discovery.ucl.ac.uk/id/eprint/10192390/> .
<https://discovery.ucl.ac.uk/id/eprint/10192390/> <http://purl.org/dc/elements/1.1/title> "HTML Summary of #10192390 \n\nComparing Comparators in Generalization Bounds\n\n" .
<https://discovery.ucl.ac.uk/id/eprint/10192390/> <http://purl.org/dc/elements/1.1/format> "text/html" .
<https://discovery.ucl.ac.uk/id/eprint/10192390/> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10192390> .