{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZPZPH54CV3VNYNUX5SKAF3ELD5","short_pith_number":"pith:ZPZPH54C","canonical_record":{"source":{"id":"1806.09908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-26T11:12:58Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1ddcad55d5e4c813efc511cb16665bd8a73827811fc80bc6789dc1d1bf3e5dea","abstract_canon_sha256":"c489f8344f6beb86d303b8cb17c5aee921f2d312358b7016c7a2bfed3c48c88b"},"schema_version":"1.0"},"canonical_sha256":"cbf2f3f782aeeadc3697ec9402ec8b1f46ee054cae820a275bf5c95f0ad080a8","source":{"kind":"arxiv","id":"1806.09908","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09908","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09908v1","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09908","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZPZPH54CV3VN","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZPZPH54CV3VNYNUX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZPZPH54C","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZPZPH54CV3VNYNUX5SKAF3ELD5","target":"record","payload":{"canonical_record":{"source":{"id":"1806.09908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-26T11:12:58Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1ddcad55d5e4c813efc511cb16665bd8a73827811fc80bc6789dc1d1bf3e5dea","abstract_canon_sha256":"c489f8344f6beb86d303b8cb17c5aee921f2d312358b7016c7a2bfed3c48c88b"},"schema_version":"1.0"},"canonical_sha256":"cbf2f3f782aeeadc3697ec9402ec8b1f46ee054cae820a275bf5c95f0ad080a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:22.929074Z","signature_b64":"DagKUOdwDZ7hTkPgEAT/474SB+HKtYVIeTO9Z8tsU0IK2yGFNP9sLCOGJ5dw//BXHNbFt7paR6uZpMxcdhJMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbf2f3f782aeeadc3697ec9402ec8b1f46ee054cae820a275bf5c95f0ad080a8","last_reissued_at":"2026-05-18T00:12:22.928448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:22.928448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.09908","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":"2026-05-18T00:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6nx5dJrF9crZv1OrXf8656RI/NYoqyUF9C2HwX2VFKen/Wa2uosklaJPrEqMvN9rcxXMdP8f+P1YRyJ3ngpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:46:48.509811Z"},"content_sha256":"3f84cf9c66b9c8679715996f9f84299da3306a72f827615f94c64bec38edd87b","schema_version":"1.0","event_id":"sha256:3f84cf9c66b9c8679715996f9f84299da3306a72f827615f94c64bec38edd87b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZPZPH54CV3VNYNUX5SKAF3ELD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Manifold Structured Prediction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Alessandro Rudi, Carlo Ciliberto, Gian Maria Marconi, Lorenzo Rosasco","submitted_at":"2018-06-26T11:12:58Z","abstract_excerpt":"Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we discuss how structured prediction can be extended to a continuous scenario. Specifically, we study a structured prediction approach to manifold valued regression. We characterize a class of problems for which the considered approach is statistically consistent and study how geometric optimization can be used to compute the corresponding estimator. Promising exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09908","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":""},"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":"2026-05-18T00:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Qk1aLVjOCeWCqdRiS2fpLvq0YDPLPryKlgme2CLkFaJak1wirc7Z3d3VWmV3kJRZ6/ybG+8WOCfx66WnZHHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:46:48.510259Z"},"content_sha256":"2acc31ae28d16dd2c83bb530ec2d7e3c1be4fbd840b00a01455e0cc5d52d1b2e","schema_version":"1.0","event_id":"sha256:2acc31ae28d16dd2c83bb530ec2d7e3c1be4fbd840b00a01455e0cc5d52d1b2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5/bundle.json","state_url":"https://pith.science/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5/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":"2026-05-25T09:46:48Z","links":{"resolver":"https://pith.science/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5","bundle":"https://pith.science/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5/bundle.json","state":"https://pith.science/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPZPH54CV3VNYNUX5SKAF3ELD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZPZPH54CV3VNYNUX5SKAF3ELD5","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":"c489f8344f6beb86d303b8cb17c5aee921f2d312358b7016c7a2bfed3c48c88b","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-26T11:12:58Z","title_canon_sha256":"1ddcad55d5e4c813efc511cb16665bd8a73827811fc80bc6789dc1d1bf3e5dea"},"schema_version":"1.0","source":{"id":"1806.09908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09908","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09908v1","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09908","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZPZPH54CV3VN","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZPZPH54CV3VNYNUX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZPZPH54C","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:2acc31ae28d16dd2c83bb530ec2d7e3c1be4fbd840b00a01455e0cc5d52d1b2e","target":"graph","created_at":"2026-05-18T00:12:22Z","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":"Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we discuss how structured prediction can be extended to a continuous scenario. Specifically, we study a structured prediction approach to manifold valued regression. We characterize a class of problems for which the considered approach is statistically consistent and study how geometric optimization can be used to compute the corresponding estimator. Promising exp","authors_text":"Alessandro Rudi, Carlo Ciliberto, Gian Maria Marconi, Lorenzo Rosasco","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-26T11:12:58Z","title":"Manifold Structured Prediction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09908","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":"sha256:3f84cf9c66b9c8679715996f9f84299da3306a72f827615f94c64bec38edd87b","target":"record","created_at":"2026-05-18T00:12:22Z","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":"c489f8344f6beb86d303b8cb17c5aee921f2d312358b7016c7a2bfed3c48c88b","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-26T11:12:58Z","title_canon_sha256":"1ddcad55d5e4c813efc511cb16665bd8a73827811fc80bc6789dc1d1bf3e5dea"},"schema_version":"1.0","source":{"id":"1806.09908","kind":"arxiv","version":1}},"canonical_sha256":"cbf2f3f782aeeadc3697ec9402ec8b1f46ee054cae820a275bf5c95f0ad080a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbf2f3f782aeeadc3697ec9402ec8b1f46ee054cae820a275bf5c95f0ad080a8","first_computed_at":"2026-05-18T00:12:22.928448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:22.928448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DagKUOdwDZ7hTkPgEAT/474SB+HKtYVIeTO9Z8tsU0IK2yGFNP9sLCOGJ5dw//BXHNbFt7paR6uZpMxcdhJMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:22.929074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f84cf9c66b9c8679715996f9f84299da3306a72f827615f94c64bec38edd87b","sha256:2acc31ae28d16dd2c83bb530ec2d7e3c1be4fbd840b00a01455e0cc5d52d1b2e"],"state_sha256":"2043526a61fe47fdcf0fb15fc6e6aa704c056c255bf8b9756609fafc1ac5fa67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ULfy73XD+J9k+Q44s1A9MyBcTMAdxWlfBbcNM6euZQ2Bc9TfgS/eKFi5HRQ1xDBtJl2uccMtQEoJ3HnyDJnkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:46:48.512924Z","bundle_sha256":"87bb3caaf0ea8cb224a5926ab621bea779c3af093f9f90fa07959c67f3532007"}}