{"paper":{"title":"On Learning Parallel Pancakes with Mostly Uniform Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Daniel M. Kane, Ilias Diakonikolas, Jasper C.H. Lee, Sushrut Karmalkar, Thanasis Pittas","submitted_at":"2025-04-21T17:31:55Z","abstract_excerpt":"We study the complexity of learning $k$-mixtures of Gaussians ($k$-GMMs) on $\\mathbb{R}^d$. This task is known to have complexity $d^{\\Omega(k)}$ in full generality. To circumvent this exponential lower bound on the number of components, research has focused on learning families of GMMs satisfying additional structural properties. A natural assumption posits that the component weights are not exponentially small and that the components have the same unknown covariance. Recent work gave a $d^{O(\\log(1/w_{\\min}))}$-time algorithm for this class of GMMs, where $w_{\\min}$ is the minimum weight. Ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15251","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.15251/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"}