{"paper":{"title":"Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ayfer \\\"Ozg\\\"ur, Peter Kairouz, Wei-Ning Chen","submitted_at":"2021-06-16T07:52:14Z","abstract_excerpt":"We consider the problem of estimating a $d$-dimensional $s$-sparse discrete distribution from its samples observed under a $b$-bit communication constraint. The best-known previous result on $\\ell_2$ estimation error for this problem is $O\\left( \\frac{s\\log\\left( {d}/{s}\\right)}{n2^b}\\right)$. Surprisingly, we show that when sample size $n$ exceeds a minimum threshold $n^*(s, d, b)$, we can achieve an $\\ell_2$ estimation error of $O\\left( \\frac{s}{n2^b}\\right)$. This implies that when $n>n^*(s, d, b)$ the convergence rate does not depend on the ambient dimension $d$ and is the same as knowing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.08597","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/2106.08597/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"}