{"paper":{"title":"Sum-of-squares lower bounds for Non-Gaussian Component Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DM","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aaron Potechin, Ilias Diakonikolas, Shuo Pang, Sushrut Karmalkar","submitted_at":"2024-10-28T18:19:13Z","abstract_excerpt":"Non-Gaussian Component Analysis (NGCA) is the statistical task of finding a non-Gaussian direction in a high-dimensional dataset. Specifically, given i.i.d.\\ samples from a distribution $P^A_{v}$ on $\\mathbb{R}^n$ that behaves like a known distribution $A$ in a hidden direction $v$ and like a standard Gaussian in the orthogonal complement, the goal is to approximate the hidden direction. The standard formulation posits that the first $k-1$ moments of $A$ match those of the standard Gaussian and the $k$-th moment differs. Under mild assumptions, this problem has sample complexity $O(n)$. On the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21426","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/2410.21426/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"}