{"paper":{"title":"PCA in Data-Dependent Noise (Correlated-PCA): Nearly Optimal Finite Sample Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Namrata Vaswani, Praneeth Narayanamurthy","submitted_at":"2017-02-10T05:35:36Z","abstract_excerpt":"We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated. Under a bounded-ness assumption on the true data and the noise, and a simple assumption on data-noise correlation, we obtain a nearly optimal sample complexity bound for the most commonly used PCA solution, singular value decomposition (SVD). This bound is a significant improvement over the bound obtained by Vaswani and Guo in recent work (NIPS 2016) where this \"correlated-PCA\" problem was first studied; and it holds under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03070","kind":"arxiv","version":3},"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"}