{"paper":{"title":"Optimal Sketching for Trace Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Hai Pham, Qiuyi (Richard) Zhang, Shuli Jiang","submitted_at":"2021-11-01T02:36:18Z","abstract_excerpt":"Matrix trace estimation is ubiquitous in machine learning applications and has traditionally relied on Hutchinson's method, which requires $O(\\log(1/\\delta)/\\epsilon^2)$ matrix-vector product queries to achieve a $(1 \\pm \\epsilon)$-multiplicative approximation to $\\text{tr}(A)$ with failure probability $\\delta$ on positive-semidefinite input matrices $A$. Recently, the Hutch++ algorithm was proposed, which reduces the number of matrix-vector queries from $O(1/\\epsilon^2)$ to the optimal $O(1/\\epsilon)$, and the algorithm succeeds with constant probability. However, in the high probability sett"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.00664","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/2111.00664/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"}