{"paper":{"title":"Bayes meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Badr-Eddine Ch\\'erief-Abdellatif, Charles Riou, Pierre Alquier","submitted_at":"2023-02-23T00:07:03Z","abstract_excerpt":"Bernstein's condition is a key assumption that guarantees fast rates in machine learning. For example, the Gibbs algorithm with prior $\\pi$ has an excess risk in $O(d_{\\pi}/n)$, as opposed to the standard $O(\\sqrt{d_{\\pi}/n})$, where $n$ denotes the number of observations and $d_{\\pi}$ is a complexity parameter which depends on the prior $\\pi$. In this paper, we examine the Gibbs algorithm in the context of meta-learning, i.e., when learning the prior $\\pi$ from $T$ tasks (with $n$ observations each) generated by a meta distribution. Our main result is that Bernstein's condition always holds a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11709","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.11709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}