{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DNPESTJ7TUL35P3UCSNFU7JWSR","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":"d889cc8196587aa3992d1694bc3a1b293a67d3c4b440e584ddf9ac20beb2decb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-05-04T17:25:52Z","title_canon_sha256":"05d416240aeafc8e48f95325f63ebfacf0fc624b118517f8cbc6e3891bf592b5"},"schema_version":"1.0","source":{"id":"1105.0875","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0875","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0875v2","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0875","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"DNPESTJ7TUL3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DNPESTJ7TUL35P3U","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DNPESTJ7","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:108c468f6f45a4714d1c66d30f1f5818e6d76e9c3839c6d62b538cb65f01c916","target":"graph","created_at":"2026-05-18T03:22:08Z","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 compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.","authors_text":"Dean P. Foster, Lyle H. Ungar, Paramveer S. Dhillon, Sham M. Kakade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-05-04T17:25:52Z","title":"A Risk Comparison of Ordinary Least Squares vs Ridge Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0875","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":"sha256:6819a3803ea9a2bf8f527677daaf31aa0fd9dc7f46a45c06714387f1d17b05d9","target":"record","created_at":"2026-05-18T03:22:08Z","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":"d889cc8196587aa3992d1694bc3a1b293a67d3c4b440e584ddf9ac20beb2decb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-05-04T17:25:52Z","title_canon_sha256":"05d416240aeafc8e48f95325f63ebfacf0fc624b118517f8cbc6e3891bf592b5"},"schema_version":"1.0","source":{"id":"1105.0875","kind":"arxiv","version":2}},"canonical_sha256":"1b5e494d3f9d17bebf74149a5a7d36946b4b850f4fddfa91f964005a2390ab49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b5e494d3f9d17bebf74149a5a7d36946b4b850f4fddfa91f964005a2390ab49","first_computed_at":"2026-05-18T03:22:08.251968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:08.251968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"801byx6A3AlIEEKt0cD/uc7ylUTJZBmBAzEd1ZiaFTrU4ZOIcYHq1IZt+axsoxqBb0FwfKMWPUtFtDvjA/fgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:08.252757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0875","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6819a3803ea9a2bf8f527677daaf31aa0fd9dc7f46a45c06714387f1d17b05d9","sha256:108c468f6f45a4714d1c66d30f1f5818e6d76e9c3839c6d62b538cb65f01c916"],"state_sha256":"87a59b786f76ed7563c414e43c318a698d98b3d11174ee65dded659f21528169"}