{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5XD4QFI5LHWNAUEXG4M7RVE323","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"83a8d0a39da831a88832615a1f8e8e2b571614275ea2a410554d8d2e781fa639","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-02-23T18:02:53Z","title_canon_sha256":"097d08fd7d2f451be1e87195a68e0bb3c96712df5bd08219da513d125a6ac1db"},"schema_version":"1.0","source":{"id":"1102.4807","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4807","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4807v3","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4807","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"5XD4QFI5LHWN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5XD4QFI5LHWNAUEX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5XD4QFI5","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:c8a6d7fa5982665a22c8d7fd423d748171e38bf560df2d6742ed0f6f0bf488da","target":"graph","created_at":"2026-05-18T03:49:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\\mathfrak{X}$ of the sum of an approximately) low rank matrix $\\Theta^\\star$ with a second matrix $\\Gamma^\\star$ endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including factor analysis, multi-task regression, and robust covariance estimation. We derive a general theorem that bounds the Frobenius norm error for an estimate of the pair ","authors_text":"Alekh Agarwal, Martin J. Wainwright, Sahand N. Negahban","cross_cats":["cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-02-23T18:02:53Z","title":"Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4807","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:74f9e6ed3856ba67bb2ac42bbd45f35edea07e49916301f770b1c4e6e9df9743","target":"record","created_at":"2026-05-18T03:49:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"83a8d0a39da831a88832615a1f8e8e2b571614275ea2a410554d8d2e781fa639","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-02-23T18:02:53Z","title_canon_sha256":"097d08fd7d2f451be1e87195a68e0bb3c96712df5bd08219da513d125a6ac1db"},"schema_version":"1.0","source":{"id":"1102.4807","kind":"arxiv","version":3}},"canonical_sha256":"edc7c8151d59ecd050973719f8d49bd6cd5dd6bc009ebd4b5283ce777cfd75ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edc7c8151d59ecd050973719f8d49bd6cd5dd6bc009ebd4b5283ce777cfd75ca","first_computed_at":"2026-05-18T03:49:12.073432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:12.073432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w88bcswOFdAGrTR5Pb8VLhZBm7rKXDFYMMkkk6VNXKTi87zML2y1Oo1QUf4/Qo78ps64S1r/kWsVjrvNZ+FGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:12.074128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4807","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74f9e6ed3856ba67bb2ac42bbd45f35edea07e49916301f770b1c4e6e9df9743","sha256:c8a6d7fa5982665a22c8d7fd423d748171e38bf560df2d6742ed0f6f0bf488da"],"state_sha256":"ee244052fa8d9226ce1f25d6d04edd8eb310708991f5f7657fe2b943cd22a245"}