{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IE3MJZX4DXUFRQJOIIVCLQUZMI","short_pith_number":"pith:IE3MJZX4","canonical_record":{"source":{"id":"1709.08104","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-23T19:12:41Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"d5a38b455de2e42dc0bef59be272596e16c7f934b54a5bc0ab6ba2e4c09d3e8d","abstract_canon_sha256":"18bce69db4cfa5be86258ddf4d41e940a7c9c498a21cec4a8ba491bea9eec918"},"schema_version":"1.0"},"canonical_sha256":"4136c4e6fc1de858c12e422a25c29962179a702ac148be42d2dc8e843c1058d0","source":{"kind":"arxiv","id":"1709.08104","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08104","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08104v2","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08104","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"IE3MJZX4DXUF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IE3MJZX4DXUFRQJO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IE3MJZX4","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IE3MJZX4DXUFRQJOIIVCLQUZMI","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08104","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-23T19:12:41Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"d5a38b455de2e42dc0bef59be272596e16c7f934b54a5bc0ab6ba2e4c09d3e8d","abstract_canon_sha256":"18bce69db4cfa5be86258ddf4d41e940a7c9c498a21cec4a8ba491bea9eec918"},"schema_version":"1.0"},"canonical_sha256":"4136c4e6fc1de858c12e422a25c29962179a702ac148be42d2dc8e843c1058d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:29.751769Z","signature_b64":"mn4xJdm4PkpUFG9pueSIUvpQVcjvoyk+aWzYg8cXC1fAMpw30K7of8dXFmmkfnFf9VJ/sD8ouKMJFjlkE4vNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4136c4e6fc1de858c12e422a25c29962179a702ac148be42d2dc8e843c1058d0","last_reissued_at":"2026-05-18T00:33:29.751224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:29.751224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08104","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":"2026-05-18T00:33:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pltIrnrbxF3G5myMYNHhgCXPaH5KxsMfxeJJh/Yc0agcZKdw/slJ+7JXduRWDuu3vg6j5ooJVan1zxxI8Gr9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:43:00.234430Z"},"content_sha256":"061698a1ae16fb6a9623f754d5e14ca8794a1c37393c3ad02eab03a7e1cc98c8","schema_version":"1.0","event_id":"sha256:061698a1ae16fb6a9623f754d5e14ca8794a1c37393c3ad02eab03a7e1cc98c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IE3MJZX4DXUFRQJOIIVCLQUZMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Principal Components Regression, Random Projections, and Column Subsampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Martin Slawski","submitted_at":"2017-09-23T19:12:41Z","abstract_excerpt":"Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be computationally demanding for large data sets. While random projections do not possess the optimality properties of the leading principal subspace, they are computationally appealing and hence have become increasingly popular in recent years. In this paper, we present an analysis showing that for random projections satisfying a Johnson-Lindenstrauss embedding prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08104","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":"2026-05-18T00:33:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iXwmvrVei9KwXEwy5g+6ffdF9nLgy1IazvA5nOO9kESskA2jWUwaRKa/OLgyWkwOy6kByxynZf6hfV2U2jCEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:43:00.234804Z"},"content_sha256":"b82dfae707446785bbb991de0039bb1f18c3da6e024c15f7a899fc8f1a53a7d0","schema_version":"1.0","event_id":"sha256:b82dfae707446785bbb991de0039bb1f18c3da6e024c15f7a899fc8f1a53a7d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI/bundle.json","state_url":"https://pith.science/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI/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":"2026-07-02T22:43:00Z","links":{"resolver":"https://pith.science/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI","bundle":"https://pith.science/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI/bundle.json","state":"https://pith.science/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IE3MJZX4DXUFRQJOIIVCLQUZMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IE3MJZX4DXUFRQJOIIVCLQUZMI","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":"18bce69db4cfa5be86258ddf4d41e940a7c9c498a21cec4a8ba491bea9eec918","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-23T19:12:41Z","title_canon_sha256":"d5a38b455de2e42dc0bef59be272596e16c7f934b54a5bc0ab6ba2e4c09d3e8d"},"schema_version":"1.0","source":{"id":"1709.08104","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08104","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08104v2","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08104","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"IE3MJZX4DXUF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IE3MJZX4DXUFRQJO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IE3MJZX4","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:b82dfae707446785bbb991de0039bb1f18c3da6e024c15f7a899fc8f1a53a7d0","target":"graph","created_at":"2026-05-18T00:33:29Z","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":"Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be computationally demanding for large data sets. While random projections do not possess the optimality properties of the leading principal subspace, they are computationally appealing and hence have become increasingly popular in recent years. In this paper, we present an analysis showing that for random projections satisfying a Johnson-Lindenstrauss embedding prop","authors_text":"Martin Slawski","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-23T19:12:41Z","title":"On Principal Components Regression, Random Projections, and Column Subsampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08104","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":"sha256:061698a1ae16fb6a9623f754d5e14ca8794a1c37393c3ad02eab03a7e1cc98c8","target":"record","created_at":"2026-05-18T00:33:29Z","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":"18bce69db4cfa5be86258ddf4d41e940a7c9c498a21cec4a8ba491bea9eec918","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-09-23T19:12:41Z","title_canon_sha256":"d5a38b455de2e42dc0bef59be272596e16c7f934b54a5bc0ab6ba2e4c09d3e8d"},"schema_version":"1.0","source":{"id":"1709.08104","kind":"arxiv","version":2}},"canonical_sha256":"4136c4e6fc1de858c12e422a25c29962179a702ac148be42d2dc8e843c1058d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4136c4e6fc1de858c12e422a25c29962179a702ac148be42d2dc8e843c1058d0","first_computed_at":"2026-05-18T00:33:29.751224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:29.751224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mn4xJdm4PkpUFG9pueSIUvpQVcjvoyk+aWzYg8cXC1fAMpw30K7of8dXFmmkfnFf9VJ/sD8ouKMJFjlkE4vNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:29.751769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08104","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:061698a1ae16fb6a9623f754d5e14ca8794a1c37393c3ad02eab03a7e1cc98c8","sha256:b82dfae707446785bbb991de0039bb1f18c3da6e024c15f7a899fc8f1a53a7d0"],"state_sha256":"cd4511900891c4a0b4652bb577cd2ceac996d53914c67feea9357ce8faaded9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IbIcJ88gdr0o+Dco7MZMAbMNNSAJjH8PBQ/8KD6I/yhasAlzfwgDDogZNUE7yjj2z+11VR3DNO1ROcFrPa+ADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T22:43:00.236727Z","bundle_sha256":"9f5c995abdb2f0193fafb22c7345aaa3ad899c523920042716058cec33fc9113"}}