{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:S5YJADIYPESLPYTPUPFBIOB7A2","short_pith_number":"pith:S5YJADIY","canonical_record":{"source":{"id":"2108.08993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-08-20T04:14:18Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"cf3170c44ebc42a5fdd6c40a4095b4fd48938c793067646e6740a28a1146847d","abstract_canon_sha256":"a0d2fe07611a5fa567ae6ff8b856cbb0143f6c1caab39239fe5671a9dc7d125e"},"schema_version":"1.0"},"canonical_sha256":"9770900d187924b7e26fa3ca14383f06878bb16d5da76e5a141c5ad772dcba74","source":{"kind":"arxiv","id":"2108.08993","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.08993","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"2108.08993v1","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.08993","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"S5YJADIYPESL","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"pith_short_16","alias_value":"S5YJADIYPESLPYTP","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"pith_short_8","alias_value":"S5YJADIY","created_at":"2026-07-05T03:07:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:S5YJADIYPESLPYTPUPFBIOB7A2","target":"record","payload":{"canonical_record":{"source":{"id":"2108.08993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-08-20T04:14:18Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"cf3170c44ebc42a5fdd6c40a4095b4fd48938c793067646e6740a28a1146847d","abstract_canon_sha256":"a0d2fe07611a5fa567ae6ff8b856cbb0143f6c1caab39239fe5671a9dc7d125e"},"schema_version":"1.0"},"canonical_sha256":"9770900d187924b7e26fa3ca14383f06878bb16d5da76e5a141c5ad772dcba74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:07:32.642384Z","signature_b64":"vII+au54Az3ZqdpqZrAQioEXBJT/8UzL5VweygmgAciXutciyshGzRFxkcSpNUDnXzAdaL8NChebGRNYjIUSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9770900d187924b7e26fa3ca14383f06878bb16d5da76e5a141c5ad772dcba74","last_reissued_at":"2026-07-05T03:07:32.641939Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:07:32.641939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.08993","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CoCnilBAUpbaKJX94Xc0yucohNn6SfnDChXCpGNRoMPZ8OZxfFBuwJLJhkA32AH5WZA03pfMXfd3CBBxB3lSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:20:25.957364Z"},"content_sha256":"94bfd0b35624cc2c08990214a210cb75969f09a1575fe3c9fb6601be6ae734e9","schema_version":"1.0","event_id":"sha256:94bfd0b35624cc2c08990214a210cb75969f09a1575fe3c9fb6601be6ae734e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:S5YJADIYPESLPYTPUPFBIOB7A2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributionally Robust Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ioannis Ch. Paschalidis, Ruidi Chen","submitted_at":"2021-08-20T04:14:18Z","abstract_excerpt":"This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental properties of the Wasserstein metric and the DRO formulation, we explore duality to arrive at tractable formulations and develop finite-sample, as well as asymptotic, performance guarantees. We consider a series of learning problems, including (i) distributionally robust linear regression; (ii) distributionally robust regression with group structure in the pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08993","kind":"arxiv","version":1},"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/2108.08993/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":"2026-07-05T03:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qk4f+2cdkRZ8ITpZSl8GUoPl813HoUuyi3GSA9UOh0l2eIuX5HwJz49xc9bl8LJkNtgg8zjiU1rKKLZRf/e4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:20:25.957840Z"},"content_sha256":"42ea8340047553bdd69392764443ba1824a7b3a546ff84c8ecbca3453478dcb6","schema_version":"1.0","event_id":"sha256:42ea8340047553bdd69392764443ba1824a7b3a546ff84c8ecbca3453478dcb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5YJADIYPESLPYTPUPFBIOB7A2/bundle.json","state_url":"https://pith.science/pith/S5YJADIYPESLPYTPUPFBIOB7A2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5YJADIYPESLPYTPUPFBIOB7A2/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":"2026-08-15T08:20:25Z","links":{"resolver":"https://pith.science/pith/S5YJADIYPESLPYTPUPFBIOB7A2","bundle":"https://pith.science/pith/S5YJADIYPESLPYTPUPFBIOB7A2/bundle.json","state":"https://pith.science/pith/S5YJADIYPESLPYTPUPFBIOB7A2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5YJADIYPESLPYTPUPFBIOB7A2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:S5YJADIYPESLPYTPUPFBIOB7A2","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":"a0d2fe07611a5fa567ae6ff8b856cbb0143f6c1caab39239fe5671a9dc7d125e","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-08-20T04:14:18Z","title_canon_sha256":"cf3170c44ebc42a5fdd6c40a4095b4fd48938c793067646e6740a28a1146847d"},"schema_version":"1.0","source":{"id":"2108.08993","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.08993","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"2108.08993v1","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.08993","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"S5YJADIYPESL","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"pith_short_16","alias_value":"S5YJADIYPESLPYTP","created_at":"2026-07-05T03:07:32Z"},{"alias_kind":"pith_short_8","alias_value":"S5YJADIY","created_at":"2026-07-05T03:07:32Z"}],"graph_snapshots":[{"event_id":"sha256:42ea8340047553bdd69392764443ba1824a7b3a546ff84c8ecbca3453478dcb6","target":"graph","created_at":"2026-07-05T03:07:32Z","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/2108.08993/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental properties of the Wasserstein metric and the DRO formulation, we explore duality to arrive at tractable formulations and develop finite-sample, as well as asymptotic, performance guarantees. We consider a series of learning problems, including (i) distributionally robust linear regression; (ii) distributionally robust regression with group structure in the pre","authors_text":"Ioannis Ch. Paschalidis, Ruidi Chen","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-08-20T04:14:18Z","title":"Distributionally Robust Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08993","kind":"arxiv","version":1},"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":"sha256:94bfd0b35624cc2c08990214a210cb75969f09a1575fe3c9fb6601be6ae734e9","target":"record","created_at":"2026-07-05T03:07:32Z","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":"a0d2fe07611a5fa567ae6ff8b856cbb0143f6c1caab39239fe5671a9dc7d125e","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-08-20T04:14:18Z","title_canon_sha256":"cf3170c44ebc42a5fdd6c40a4095b4fd48938c793067646e6740a28a1146847d"},"schema_version":"1.0","source":{"id":"2108.08993","kind":"arxiv","version":1}},"canonical_sha256":"9770900d187924b7e26fa3ca14383f06878bb16d5da76e5a141c5ad772dcba74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9770900d187924b7e26fa3ca14383f06878bb16d5da76e5a141c5ad772dcba74","first_computed_at":"2026-07-05T03:07:32.641939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:07:32.641939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vII+au54Az3ZqdpqZrAQioEXBJT/8UzL5VweygmgAciXutciyshGzRFxkcSpNUDnXzAdaL8NChebGRNYjIUSDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:07:32.642384Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.08993","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94bfd0b35624cc2c08990214a210cb75969f09a1575fe3c9fb6601be6ae734e9","sha256:42ea8340047553bdd69392764443ba1824a7b3a546ff84c8ecbca3453478dcb6"],"state_sha256":"73fc462ee0e3a3dffdc43aee223eaf08ef59cce4acde0bbb1b9e9f8c28f47dbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILVego62GoNeuJQOyE8bYXbXbWAp3OIVbw8guMyw9WSSACX7jFqBedhxbVP4xTTko7u6PNYhXYxup8U+Pye9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T08:20:25.962144Z","bundle_sha256":"8d3fb1b4818aeb2bd2692470e65f23987e4eee2b5fef5f6df772813a75495d92"}}