{"paper":{"title":"Streaming PCA: Matching Matrix Bernstein and Near-Optimal Finite Sample Guarantees for Oja's Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aaron Sidford, Chi Jin, Praneeth Netrapalli, Prateek Jain, Sham M. Kakade","submitted_at":"2016-02-22T20:30:37Z","abstract_excerpt":"This work provides improved guarantees for streaming principle component analysis (PCA). Given $A_1, \\ldots, A_n\\in \\mathbb{R}^{d\\times d}$ sampled independently from distributions satisfying $\\mathbb{E}[A_i] = \\Sigma$ for $\\Sigma \\succeq \\mathbf{0}$, this work provides an $O(d)$-space linear-time single-pass streaming algorithm for estimating the top eigenvector of $\\Sigma$. The algorithm nearly matches (and in certain cases improves upon) the accuracy obtained by the standard batch method that computes top eigenvector of the empirical covariance $\\frac{1}{n} \\sum_{i \\in [n]} A_i$ as analyzed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06929","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":""},"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"}