{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RF4YUFC4IA7YL26UT6P4GTMFZX","short_pith_number":"pith:RF4YUFC4","canonical_record":{"source":{"id":"2311.06960","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-11-12T20:57:30Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"02b1a2d62a16496bc1a4030c2e06082b86070daea65b938d961f3cad89e2ff4a","abstract_canon_sha256":"1d4aa1e639f2319de8aeea8202971afbbd23563aab770ad44b70ac6313d1c32a"},"schema_version":"1.0"},"canonical_sha256":"89798a145c403f85ebd49f9fc34d85cde40ecb9e6e432a991263b737c0a0e2b0","source":{"kind":"arxiv","id":"2311.06960","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06960","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06960v2","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06960","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"RF4YUFC4IA7Y","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"pith_short_16","alias_value":"RF4YUFC4IA7YL26U","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"pith_short_8","alias_value":"RF4YUFC4","created_at":"2026-07-05T09:17:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RF4YUFC4IA7YL26UT6P4GTMFZX","target":"record","payload":{"canonical_record":{"source":{"id":"2311.06960","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-11-12T20:57:30Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"02b1a2d62a16496bc1a4030c2e06082b86070daea65b938d961f3cad89e2ff4a","abstract_canon_sha256":"1d4aa1e639f2319de8aeea8202971afbbd23563aab770ad44b70ac6313d1c32a"},"schema_version":"1.0"},"canonical_sha256":"89798a145c403f85ebd49f9fc34d85cde40ecb9e6e432a991263b737c0a0e2b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:17:34.617305Z","signature_b64":"Jw6fhJmZxfWi7gSvSnWjFXbXj8IpCf4qB9OWz6RotgA/mqTheMcg1W3LH+E2VfMpVujaevWoTuYeDRbxDhhoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89798a145c403f85ebd49f9fc34d85cde40ecb9e6e432a991263b737c0a0e2b0","last_reissued_at":"2026-07-05T09:17:34.616753Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:17:34.616753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.06960","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":"2026-07-05T09:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/tU8lvhrVOcEDjVtN9dNfZomB8niKqxJzPKUuHokovWhkABRsYAWDnTtxN+IU2WRpSd/RqohhcyyGDaPusgzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:42:38.507599Z"},"content_sha256":"cb0fcaf0ab722b5819f6fbb3dd355029cef44136792b06f602d101aed7344e94","schema_version":"1.0","event_id":"sha256:cb0fcaf0ab722b5819f6fbb3dd355029cef44136792b06f602d101aed7344e94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RF4YUFC4IA7YL26UT6P4GTMFZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Regression over Averaged Uncertainty","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Dimitris Bertsimas, Yu Ma","submitted_at":"2023-11-12T20:57:30Z","abstract_excerpt":"We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this formulation recovers ridge regression exactly and establishes the missing link between robust optimization and the mean squared error approaches for existing regression problems. We further demonstrate that the condition of this equivalence relies on the geometric properties of the defined uncertainty set. We provide exact, closed-form, in some cases, analytica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06960","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.06960/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAuHcsK4KO8Abs3rrb2w124P7mRYGd6tpR2DHZk2ZtCaWa2nIS7pNOwgVUh0jajTeeGn2U5jX7bKDMqAzoVVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:42:38.508359Z"},"content_sha256":"3b2f0365f9329b20c7f48bf3eff258de9594d82a3551c512c43c00f73de92ce7","schema_version":"1.0","event_id":"sha256:3b2f0365f9329b20c7f48bf3eff258de9594d82a3551c512c43c00f73de92ce7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RF4YUFC4IA7YL26UT6P4GTMFZX/bundle.json","state_url":"https://pith.science/pith/RF4YUFC4IA7YL26UT6P4GTMFZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RF4YUFC4IA7YL26UT6P4GTMFZX/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":"2026-08-11T01:42:38Z","links":{"resolver":"https://pith.science/pith/RF4YUFC4IA7YL26UT6P4GTMFZX","bundle":"https://pith.science/pith/RF4YUFC4IA7YL26UT6P4GTMFZX/bundle.json","state":"https://pith.science/pith/RF4YUFC4IA7YL26UT6P4GTMFZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RF4YUFC4IA7YL26UT6P4GTMFZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RF4YUFC4IA7YL26UT6P4GTMFZX","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":"1d4aa1e639f2319de8aeea8202971afbbd23563aab770ad44b70ac6313d1c32a","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-11-12T20:57:30Z","title_canon_sha256":"02b1a2d62a16496bc1a4030c2e06082b86070daea65b938d961f3cad89e2ff4a"},"schema_version":"1.0","source":{"id":"2311.06960","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06960","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06960v2","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06960","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"RF4YUFC4IA7Y","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"pith_short_16","alias_value":"RF4YUFC4IA7YL26U","created_at":"2026-07-05T09:17:34Z"},{"alias_kind":"pith_short_8","alias_value":"RF4YUFC4","created_at":"2026-07-05T09:17:34Z"}],"graph_snapshots":[{"event_id":"sha256:3b2f0365f9329b20c7f48bf3eff258de9594d82a3551c512c43c00f73de92ce7","target":"graph","created_at":"2026-07-05T09:17:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.06960/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this formulation recovers ridge regression exactly and establishes the missing link between robust optimization and the mean squared error approaches for existing regression problems. We further demonstrate that the condition of this equivalence relies on the geometric properties of the defined uncertainty set. We provide exact, closed-form, in some cases, analytica","authors_text":"Dimitris Bertsimas, Yu Ma","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-11-12T20:57:30Z","title":"Robust Regression over Averaged Uncertainty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06960","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:cb0fcaf0ab722b5819f6fbb3dd355029cef44136792b06f602d101aed7344e94","target":"record","created_at":"2026-07-05T09:17:34Z","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":"1d4aa1e639f2319de8aeea8202971afbbd23563aab770ad44b70ac6313d1c32a","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-11-12T20:57:30Z","title_canon_sha256":"02b1a2d62a16496bc1a4030c2e06082b86070daea65b938d961f3cad89e2ff4a"},"schema_version":"1.0","source":{"id":"2311.06960","kind":"arxiv","version":2}},"canonical_sha256":"89798a145c403f85ebd49f9fc34d85cde40ecb9e6e432a991263b737c0a0e2b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89798a145c403f85ebd49f9fc34d85cde40ecb9e6e432a991263b737c0a0e2b0","first_computed_at":"2026-07-05T09:17:34.616753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:17:34.616753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jw6fhJmZxfWi7gSvSnWjFXbXj8IpCf4qB9OWz6RotgA/mqTheMcg1W3LH+E2VfMpVujaevWoTuYeDRbxDhhoAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:17:34.617305Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.06960","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb0fcaf0ab722b5819f6fbb3dd355029cef44136792b06f602d101aed7344e94","sha256:3b2f0365f9329b20c7f48bf3eff258de9594d82a3551c512c43c00f73de92ce7"],"state_sha256":"872790d62c9e93c133513691932a4a94c59bb8998e21d8421434de696489c82c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qqHKUy33L2OWUF5n23ZIJCGnirUh+fun5AuGSQZSoAVgFOextyxcc3N3SZwWhVgKIZqI21tuBGIZo2ECORGLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T01:42:38.515172Z","bundle_sha256":"077ac8727c27368685d8128c2c0abb4e780ee81d4c2af13a893fd847ef55a78f"}}