{"paper":{"title":"A Tight Analysis of Hutchinson's Diagonal Estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"Christopher Musco, Prathamesh Dharangutte","submitted_at":"2022-08-05T16:39:27Z","abstract_excerpt":"Let $\\mathbf{A}\\in \\mathbb{R}^{n\\times n}$ be a matrix with diagonal $\\text{diag}(\\mathbf{A})$ and let $\\bar{\\mathbf{A}}$ be $\\mathbf{A}$ with its diagonal set to all zeros. We show that Hutchinson's estimator run for $m$ iterations returns a diagonal estimate $\\tilde{d}\\in \\mathbb{R}^n$ such that with probability $(1-\\delta)$, $$\\|\\tilde{d} - \\text{diag}(\\mathbf{A})\\|_2 \\leq c\\sqrt{\\frac{\\log(2/\\delta)}{m}}\\|\\bar{\\mathbf{A}}\\|_F,$$ where $c$ is a fixed constant independent of all other parameters. This results improves on a recent result of [Baston and Nakatsukasa, 2022] by a $\\log(n)$ factor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.03268","kind":"arxiv","version":2},"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/2208.03268/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"}