{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OFFIFUTLXBWGCKRPZJ4HOPW6ND","short_pith_number":"pith:OFFIFUTL","canonical_record":{"source":{"id":"1610.09307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-28T16:37:39Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"fda34a512b6bfc9b727e6bda3e28a937a3a1acaea642f8750fa510c6637e1d1c","abstract_canon_sha256":"884cd0f4934b783c119501b4ea23e3f97faf6bd38ab8f76d5689192b0f8682b0"},"schema_version":"1.0"},"canonical_sha256":"714a82d26bb86c612a2fca78773ede68f920f96e3804b3af796383d8a0894050","source":{"kind":"arxiv","id":"1610.09307","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09307","created_at":"2026-05-18T01:00:52Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09307v2","created_at":"2026-05-18T01:00:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09307","created_at":"2026-05-18T01:00:52Z"},{"alias_kind":"pith_short_12","alias_value":"OFFIFUTLXBWG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OFFIFUTLXBWGCKRP","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OFFIFUTL","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OFFIFUTLXBWGCKRPZJ4HOPW6ND","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-28T16:37:39Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"fda34a512b6bfc9b727e6bda3e28a937a3a1acaea642f8750fa510c6637e1d1c","abstract_canon_sha256":"884cd0f4934b783c119501b4ea23e3f97faf6bd38ab8f76d5689192b0f8682b0"},"schema_version":"1.0"},"canonical_sha256":"714a82d26bb86c612a2fca78773ede68f920f96e3804b3af796383d8a0894050","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:52.190448Z","signature_b64":"5dW7RNixuisV7SiYpemUR/8F1j0Hq0ML1pZu81eEaHNy14V1Q8/d78sEcmpbCyqWjKtOnOhtX0bkOPoRLdLfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"714a82d26bb86c612a2fca78773ede68f920f96e3804b3af796383d8a0894050","last_reissued_at":"2026-05-18T01:00:52.189882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:52.189882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09307","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3mCKCpeAMwvOwuHBsS895EKJAXbD2ubrWr2Oj7dmtYXhA0xf/kXsAA8zLEgwuNiG36rlLB/GZ/GHDa6EdjksAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:09:36.896113Z"},"content_sha256":"6471466931c3822ae66596dbfa3e71e8c95c4820bd8409e99a092d2bcf6ef0aa","schema_version":"1.0","event_id":"sha256:6471466931c3822ae66596dbfa3e71e8c95c4820bd8409e99a092d2bcf6ef0aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OFFIFUTLXBWGCKRPZJ4HOPW6ND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlated-PCA: Principal Components' Analysis when Data and Noise are Correlated","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Han Guo, Namrata Vaswani","submitted_at":"2016-10-28T16:37:39Z","abstract_excerpt":"Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to the best of our knowledge, all existing theoretical guarantees for it assume that the data and the corrupting noise are mutually independent, or at least uncorrelated. This is valid in practice often, but not always. In this paper, we study the PCA problem in the setting where the data and noise can be correlated. Such noise is often also referred to as \"data-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09307","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEmUNeg7tywdi10Hn3erP1FluEHdxcotjK05BZZUNQSdkxjs2xJVwP7DgB14wR1ddizgO+unGkpZvqsnBYRjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:09:36.896478Z"},"content_sha256":"55bb98e734e9996cd9a177a5cf602bc7bd1a4c1395a6919b96d315d657c9c784","schema_version":"1.0","event_id":"sha256:55bb98e734e9996cd9a177a5cf602bc7bd1a4c1395a6919b96d315d657c9c784"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND/bundle.json","state_url":"https://pith.science/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T06:09:36Z","links":{"resolver":"https://pith.science/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND","bundle":"https://pith.science/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND/bundle.json","state":"https://pith.science/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFFIFUTLXBWGCKRPZJ4HOPW6ND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OFFIFUTLXBWGCKRPZJ4HOPW6ND","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":"884cd0f4934b783c119501b4ea23e3f97faf6bd38ab8f76d5689192b0f8682b0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-28T16:37:39Z","title_canon_sha256":"fda34a512b6bfc9b727e6bda3e28a937a3a1acaea642f8750fa510c6637e1d1c"},"schema_version":"1.0","source":{"id":"1610.09307","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09307","created_at":"2026-05-18T01:00:52Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09307v2","created_at":"2026-05-18T01:00:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09307","created_at":"2026-05-18T01:00:52Z"},{"alias_kind":"pith_short_12","alias_value":"OFFIFUTLXBWG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OFFIFUTLXBWGCKRP","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OFFIFUTL","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:55bb98e734e9996cd9a177a5cf602bc7bd1a4c1395a6919b96d315d657c9c784","target":"graph","created_at":"2026-05-18T01:00:52Z","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":"Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to the best of our knowledge, all existing theoretical guarantees for it assume that the data and the corrupting noise are mutually independent, or at least uncorrelated. This is valid in practice often, but not always. In this paper, we study the PCA problem in the setting where the data and noise can be correlated. Such noise is often also referred to as \"data-","authors_text":"Han Guo, Namrata Vaswani","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-28T16:37:39Z","title":"Correlated-PCA: Principal Components' Analysis when Data and Noise are Correlated"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09307","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":"sha256:6471466931c3822ae66596dbfa3e71e8c95c4820bd8409e99a092d2bcf6ef0aa","target":"record","created_at":"2026-05-18T01:00:52Z","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":"884cd0f4934b783c119501b4ea23e3f97faf6bd38ab8f76d5689192b0f8682b0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-28T16:37:39Z","title_canon_sha256":"fda34a512b6bfc9b727e6bda3e28a937a3a1acaea642f8750fa510c6637e1d1c"},"schema_version":"1.0","source":{"id":"1610.09307","kind":"arxiv","version":2}},"canonical_sha256":"714a82d26bb86c612a2fca78773ede68f920f96e3804b3af796383d8a0894050","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"714a82d26bb86c612a2fca78773ede68f920f96e3804b3af796383d8a0894050","first_computed_at":"2026-05-18T01:00:52.189882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:52.189882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dW7RNixuisV7SiYpemUR/8F1j0Hq0ML1pZu81eEaHNy14V1Q8/d78sEcmpbCyqWjKtOnOhtX0bkOPoRLdLfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:52.190448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09307","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6471466931c3822ae66596dbfa3e71e8c95c4820bd8409e99a092d2bcf6ef0aa","sha256:55bb98e734e9996cd9a177a5cf602bc7bd1a4c1395a6919b96d315d657c9c784"],"state_sha256":"1bda019f592d5632329ab0a5aff7723108df3cfea2d4fa6c53c19da7b95b47ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OD609gQFm3AISfKstsaSfwrx6BhxuZey0eAcCgd5nEa3FcQ1zmGHbfWfgkW9gIwBBs0ffaGX+7FY/6ox1PL9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:09:36.898397Z","bundle_sha256":"b878430e4cab950427c98bb475b4c80f4e8c4ddb43561b1c526bbb9f4c1f4db0"}}