{"paper":{"title":"Polynomial Estimators for High Frequency Moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Sumit Ganguly","submitted_at":"2011-04-23T12:32:22Z","abstract_excerpt":"We present an algorithm for computing $F_p$, the $p$th moment of an $n$-dimensional frequency vector of a data stream, for $2 < p < \\log (n) $, to within $1\\pm \\epsilon$ factors, $\\epsilon \\in [n^{-1/p},1]$ with high constant probability. Let $m$ be the number of stream records and $M$ be the largest magnitude of a stream update.\n  The algorithm uses space in bits $$ O(p^2\\epsilon^{-2}n^{1-2/p}E(p,n) \\log (n) \\log (nmM)/\\min(\\log (n),\\epsilon^{4/p-2}))$$ where, $E(p,n) = (1-2/p)^{-1}(1-n^{-4(1-2/p})$. Here $E(p,n)$ is $ O(1)$ for $p = 2+\\Omega(1)$ and $ O(\\log n)$ for $p = 2 + O(1/\\log (n)$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4552","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":""},"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"}