{"paper":{"title":"SoS Certificates for Sparse Singular Values and Their Applications: Robust Statistics, Subspace Distortion, and More","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Ankit Pensia, Ilias Diakonikolas, Samuel B. Hopkins, Stefan Tiegel","submitted_at":"2024-12-30T18:59:46Z","abstract_excerpt":"We study $\\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \\times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on the maximum of $\\|M u\\|$, where $u$ is a unit vector with at most $\\eta n$ nonzero entries for a given $\\eta \\in (0,1)$. This basic algorithmic primitive lies at the heart of a wide range of problems across algorithmic statistics and theoretical computer science.\n  Our algorithms certify a bound which is asymptotically smaller than the naive one, given by t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21203","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/2412.21203/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"}