{"paper":{"title":"Fitting a manifold to data in the presence of large noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","stat.TH"],"primary_cat":"math.ST","authors_text":"Charles Fefferman, Hariharan Narayanan, Matti Lassas, Sergei Ivanov","submitted_at":"2023-12-17T03:26:42Z","abstract_excerpt":"We assume that $M_0$ is a $d$-dimensional $C^{2,1}$-smooth submanifold of $R^n$. Let $K_0$ be the convex hull of $M_0,$ and $B^n_1(0)$ be the unit ball. We assume that $ M_0 \\subseteq \\partial K_0 \\subseteq B^n_1(0).$ We also suppose that $M_0$ has volume ($d$-dimensional Hausdorff measure) less or equal to $V$, reach (i.e., normal injectivity radius) greater or equal to $\\tau$.\n  Moreover, we assume that $M_0$ is $R$-exposed, that is, tangent to every point $x \\in M$ there is a closed ball of radius $R$ that contains $M$. Let $x_1, \\dots, x_N$ be independent random variables sampled from unif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.10598","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/2312.10598/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"}