{"paper":{"title":"Near-optimal algorithms for private estimation and sequential testing of collision probability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"stat.ML","authors_text":"Robert Busa-Fekete, Umar Syed","submitted_at":"2025-04-18T17:12:15Z","abstract_excerpt":"We present new algorithms for estimating and testing \\emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies $(\\alpha, \\beta)$-local differential privacy and estimates collision probability with error at most $\\epsilon$ using $\\tilde{O}\\left(\\frac{\\log(1/\\beta)}{\\alpha^2 \\epsilon^2}\\right)$ samples for $\\alpha \\le 1$, which improves over previous work by a factor of $\\frac{1}{\\alpha^2}$. We also present a sequential testing algorithm for collision probability, which can d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.13804","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/2504.13804/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"}