{"paper":{"title":"Algorithms and Hardness for Robust Subspace Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","cs.LG","math.IT"],"primary_cat":"cs.CC","authors_text":"Ankur Moitra, Moritz Hardt","submitted_at":"2012-11-05T21:39:22Z","abstract_excerpt":"We consider a fundamental problem in unsupervised learning called \\emph{subspace recovery}: given a collection of $m$ points in $\\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$ can we find it? The points contained in $T$ are called {\\em inliers} and the remaining points are {\\em outliers}. This problem has received considerable attention in computer science and in statistics. Yet efficient algorithms from computer science are not robust to {\\em adversarial} outliers, and the estimators from robust statistics are hard to compute in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1041","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}