{"paper":{"title":"New Statistical and Computational Results for Learning Junta Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.LG","authors_text":"Lorenzo Beretta","submitted_at":"2025-05-09T06:44:35Z","abstract_excerpt":"We study the problem of learning junta distributions on $\\{0, 1\\}^n$, where a distribution is a $k$-junta if its probability mass function depends on a subset of at most $k$ variables. We make two main contributions:\n  - We show that learning $k$-junta distributions is \\emph{computationally} equivalent to learning $k$-parity functions with noise (LPN), a landmark problem in computational learning theory.\n  - We design an algorithm for learning junta distributions whose statistical complexity is optimal, up to polylogarithmic factors. Computationally, our algorithm matches the complexity of pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05819","kind":"arxiv","version":3},"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/2505.05819/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"}