{"paper":{"title":"A Fourier Approach to Mixture Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Ankit Singh Rawat, Avinava Dubey, Guru Guruganesh, Manzil Zaheer, Mingda Qiao","submitted_at":"2022-10-05T17:35:46Z","abstract_excerpt":"We revisit the problem of learning mixtures of spherical Gaussians. Given samples from mixture $\\frac{1}{k}\\sum_{j=1}^{k}\\mathcal{N}(\\mu_j, I_d)$, the goal is to estimate the means $\\mu_1, \\mu_2, \\ldots, \\mu_k \\in \\mathbb{R}^d$ up to a small error. The hardness of this learning problem can be measured by the separation $\\Delta$ defined as the minimum distance between all pairs of means. Regev and Vijayaraghavan (2017) showed that with $\\Delta = \\Omega(\\sqrt{\\log k})$ separation, the means can be learned using $\\mathrm{poly}(k, d)$ samples, whereas super-polynomially many samples are required i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.02415","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.02415/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}