{"paper":{"title":"Convergence Rate of Krasulina Estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.CO","stat.TH"],"primary_cat":"stat.ML","authors_text":"Jiangning Chen","submitted_at":"2018-08-28T18:47:20Z","abstract_excerpt":"Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points $X_1, X_2,..., X_n$ are vectors drawn i.i.d. from a distribution with mean zero and covariance $\\Sigma$, where $\\Sigma$ is unknown. Let $A_n = X_nX_n^T$, then $E[A_n] = \\Sigma$. This paper consider the problem of finding the least eigenvalue and eigenvector of matrix $\\Sigma$. A classical such estimator are due to Krasulina\\cite{krasulina_method_1969}. We are going to state the convergence proof of Krasulina for the least eigenvalue and corresponding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09489","kind":"arxiv","version":4},"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"}