{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HPLMMGG7GITQUJVAKW2I2XOM2M","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":"d0547d7c2b6e3abdd71ca0832ccb7e8b592ffca84e6dd0407656a26011614439","cross_cats_sorted":["math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-10T05:35:36Z","title_canon_sha256":"62ae9510a92f310cbfa4ba6f03881c242277d174998ef740056d64039dc732e1"},"schema_version":"1.0","source":{"id":"1702.03070","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03070","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03070v3","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03070","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"HPLMMGG7GITQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HPLMMGG7GITQUJVA","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HPLMMGG7","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:86fef7ffa52bd854424e6abe8551906198313fe31edbc015b3247ab754f11b98","target":"graph","created_at":"2026-05-18T00:31:41Z","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 study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated. Under a bounded-ness assumption on the true data and the noise, and a simple assumption on data-noise correlation, we obtain a nearly optimal sample complexity bound for the most commonly used PCA solution, singular value decomposition (SVD). This bound is a significant improvement over the bound obtained by Vaswani and Guo in recent work (NIPS 2016) where this \"correlated-PCA\" problem was first studied; and it holds under","authors_text":"Namrata Vaswani, Praneeth Narayanamurthy","cross_cats":["math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-10T05:35:36Z","title":"PCA in Data-Dependent Noise (Correlated-PCA): Nearly Optimal Finite Sample Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03070","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":"sha256:95cf3d6b701612b355d4fcf6327631f96bfbe56a3d7e6e794990057b5440d4dc","target":"record","created_at":"2026-05-18T00:31:41Z","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":"d0547d7c2b6e3abdd71ca0832ccb7e8b592ffca84e6dd0407656a26011614439","cross_cats_sorted":["math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-10T05:35:36Z","title_canon_sha256":"62ae9510a92f310cbfa4ba6f03881c242277d174998ef740056d64039dc732e1"},"schema_version":"1.0","source":{"id":"1702.03070","kind":"arxiv","version":3}},"canonical_sha256":"3bd6c618df32270a26a055b48d5dccd3303af042aca43644149d0b4aae0274e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bd6c618df32270a26a055b48d5dccd3303af042aca43644149d0b4aae0274e5","first_computed_at":"2026-05-18T00:31:41.652350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:41.652350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CylJBvWae47b1MLfpuh+gdI4eQ1HDjrC+UugbyuNi9m7kk1dxGWJYFOUGBCL8s4RZvOGe1h42Rj8lQsVixrqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:41.652982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03070","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95cf3d6b701612b355d4fcf6327631f96bfbe56a3d7e6e794990057b5440d4dc","sha256:86fef7ffa52bd854424e6abe8551906198313fe31edbc015b3247ab754f11b98"],"state_sha256":"3df729b7b8c6a7ce7a3061d99dc376b6c613a4a9707db51ee708b4052b27143c"}