{"paper":{"title":"SoS Certifiability of Subgaussian Distributions and its Algorithmic Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.DS","authors_text":"Ankit Pensia, Ilias Diakonikolas, Samuel B. Hopkins, Stefan Tiegel","submitted_at":"2024-10-28T16:36:58Z","abstract_excerpt":"We prove that there is a universal constant $C>0$ so that for every $d \\in \\mathbb N$, every centered subgaussian distribution $\\mathcal D$ on $\\mathbb R^d$, and every even $p \\in \\mathbb N$, the $d$-variate polynomial $(Cp)^{p/2} \\cdot \\|v\\|_{2}^p - \\mathbb E_{X \\sim \\mathcal D} \\langle v,X\\rangle^p$ is a sum of square polynomials. This establishes that every subgaussian distribution is \\emph{SoS-certifiably subgaussian} -- a condition that yields efficient learning algorithms for a wide variety of high-dimensional statistical tasks. As a direct corollary, we obtain computationally efficient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21194","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/2410.21194/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"}