{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L7GXRES3BBYNPVKB5EOUZMOY46","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":"558ab352ba11f28f940eaef49a834f983943059544e90097470271603245e2f8","cross_cats_sorted":["cs.LG","math.IT","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-25T09:10:07Z","title_canon_sha256":"cfcd99e653c0ae20c9696a18a0b612a44288b498918f2f114cd1cb105f6fd65b"},"schema_version":"1.0","source":{"id":"1605.07784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07784","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07784v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07784","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"L7GXRES3BBYN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L7GXRES3BBYNPVKB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L7GXRES3","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:ba7f940016766d368cd152b28c73f9e02e41b62a05c52ff1d84df24f165d799b","target":"graph","created_at":"2026-05-18T01:04:27Z","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 consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and conditions on when recovery is possible (how many observations do we need, how many corruptions can we tolerate) via polynomial-time algorithms is by now understood. This paper presents and analyzes a non-convex optimization approach that greatly reduces the computational complexity of the above problems, compared to the best available algorithms. In particular, i","authors_text":"Constantine Caramanis, Dohyung Park, Xinyang Yi, Yudong Chen","cross_cats":["cs.LG","math.IT","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-25T09:10:07Z","title":"Fast Algorithms for Robust PCA via Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07784","kind":"arxiv","version":2},"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:d5a8229f8268ed65a3130ce697f2e2fdbcd9c3284ecde3d16bac5f1c45936998","target":"record","created_at":"2026-05-18T01:04:27Z","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":"558ab352ba11f28f940eaef49a834f983943059544e90097470271603245e2f8","cross_cats_sorted":["cs.LG","math.IT","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-25T09:10:07Z","title_canon_sha256":"cfcd99e653c0ae20c9696a18a0b612a44288b498918f2f114cd1cb105f6fd65b"},"schema_version":"1.0","source":{"id":"1605.07784","kind":"arxiv","version":2}},"canonical_sha256":"5fcd78925b0870d7d541e91d4cb1d8e7849b747656efa50f09b5ce7895cedc85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fcd78925b0870d7d541e91d4cb1d8e7849b747656efa50f09b5ce7895cedc85","first_computed_at":"2026-05-18T01:04:27.622719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:27.622719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/pbN0JW0B/SXJxaVfawlwN4dte8m9eAf+EOYNlTnqconKphC/lXC2nB/dIjPh8iRE0qg/1w8j5LHzr0G0c/xDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:27.623284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5a8229f8268ed65a3130ce697f2e2fdbcd9c3284ecde3d16bac5f1c45936998","sha256:ba7f940016766d368cd152b28c73f9e02e41b62a05c52ff1d84df24f165d799b"],"state_sha256":"d633465d9950afa5e75a30dd9ccd24bc9565286350e0c13a32847420b93bbab5"}