{"paper":{"title":"Near-optimal-sample estimators for spherical Gaussian mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alon Orlitsky, Ananda Theertha Suresh, Ashkan Jafarpour, Jayadev Acharya","submitted_at":"2014-02-19T17:59:55Z","abstract_excerpt":"Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient polynomial-time estimator for high-dimensional spherical Gaussian mixtures.\n  For mixtures of any $k$ $d$-dimensional spherical Gaussians, we derive an intuitive spectral-estimator that uses $\\mathcal{O}_k\\bigl(\\frac{d\\log^2d}{\\epsilon^4}\\bigr)$ samples and runs in time $\\mathcal{O}_{k,\\epsilon}(d^3\\log^5 d)$, both significantly lower than previously known. The constant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4746","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"}