{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2NYKNK7CYIGZGXY4AMAG2H6ZG2","short_pith_number":"pith:2NYKNK7C","canonical_record":{"source":{"id":"1510.08231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-28T09:18:50Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"ce20481d0854aca4afd587e17311512fd34ac5f4f78264b00f09c03e4f3c4ed4","abstract_canon_sha256":"631b9c0b8ea9f5dcbed80d10103ce019cd0d7832ce22ea072167ff108f7fe6f4"},"schema_version":"1.0"},"canonical_sha256":"d370a6abe2c20d935f1c03006d1fd93685531fe925aa0459cc1e355080def6cf","source":{"kind":"arxiv","id":"1510.08231","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08231","created_at":"2026-05-18T01:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08231v3","created_at":"2026-05-18T01:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08231","created_at":"2026-05-18T01:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"2NYKNK7CYIGZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NYKNK7CYIGZGXY4","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NYKNK7C","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2NYKNK7CYIGZGXY4AMAG2H6ZG2","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-28T09:18:50Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"ce20481d0854aca4afd587e17311512fd34ac5f4f78264b00f09c03e4f3c4ed4","abstract_canon_sha256":"631b9c0b8ea9f5dcbed80d10103ce019cd0d7832ce22ea072167ff108f7fe6f4"},"schema_version":"1.0"},"canonical_sha256":"d370a6abe2c20d935f1c03006d1fd93685531fe925aa0459cc1e355080def6cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:40.261155Z","signature_b64":"yJN5Dg/TE6dep3CoUdpxN8USG/zc/+SZvvzQGVDK35Jq5VoWcKlqs/UIbVy78vvVYz83Gt+W72Y7+Pd+/aQiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d370a6abe2c20d935f1c03006d1fd93685531fe925aa0459cc1e355080def6cf","last_reissued_at":"2026-05-18T01:00:40.260413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:40.260413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08231","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OxRZ+cFOrCbWhg07GkQgXfwv/22JZk0byZzzBeuoVu58TcrLGBF8huagT8TtQ4g8gEXRuHYsDfrnRoslVY+eBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:53:16.832272Z"},"content_sha256":"8c4deed030b116cb3f530c64582c68ab530c09c3dae800cda043ba1f5468e81e","schema_version":"1.0","event_id":"sha256:8c4deed030b116cb3f530c64582c68ab530c09c3dae800cda043ba1f5468e81e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2NYKNK7CYIGZGXY4AMAG2H6ZG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator-valued Kernels for Learning from Functional Response Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alain Rakotomamonjy (LITIS), Emmanuel Duflos (CRIStAL), Hachem Kadri (LIF), Julien Audiffren (CMLA), Philippe Preux (CRIStAL, SEQUEL), St\\'ephane Canu (LITIS)","submitted_at":"2015-10-28T09:18:50Z","abstract_excerpt":"In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08231","kind":"arxiv","version":3},"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":"2026-05-18T01:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxecOMTr4b8BPOpx5FgIdx2iWbr3STv1IKQKWLqnDdueutxaUaGb/EkAzqqbCdg6C7buJq2PJTxl2KHdV2UDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:53:16.833008Z"},"content_sha256":"72410977bc0d855459eb4aeb39425f68c0eecb2bdfec84bfec58cb4dbd177ec6","schema_version":"1.0","event_id":"sha256:72410977bc0d855459eb4aeb39425f68c0eecb2bdfec84bfec58cb4dbd177ec6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/bundle.json","state_url":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/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":"2026-05-30T07:53:16Z","links":{"resolver":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2","bundle":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/bundle.json","state":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2NYKNK7CYIGZGXY4AMAG2H6ZG2","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":"631b9c0b8ea9f5dcbed80d10103ce019cd0d7832ce22ea072167ff108f7fe6f4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-28T09:18:50Z","title_canon_sha256":"ce20481d0854aca4afd587e17311512fd34ac5f4f78264b00f09c03e4f3c4ed4"},"schema_version":"1.0","source":{"id":"1510.08231","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08231","created_at":"2026-05-18T01:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08231v3","created_at":"2026-05-18T01:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08231","created_at":"2026-05-18T01:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"2NYKNK7CYIGZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NYKNK7CYIGZGXY4","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NYKNK7C","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:72410977bc0d855459eb4aeb39425f68c0eecb2bdfec84bfec58cb4dbd177ec6","target":"graph","created_at":"2026-05-18T01:00:40Z","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":"In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when","authors_text":"Alain Rakotomamonjy (LITIS), Emmanuel Duflos (CRIStAL), Hachem Kadri (LIF), Julien Audiffren (CMLA), Philippe Preux (CRIStAL, SEQUEL), St\\'ephane Canu (LITIS)","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-28T09:18:50Z","title":"Operator-valued Kernels for Learning from Functional Response Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08231","kind":"arxiv","version":3},"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":"sha256:8c4deed030b116cb3f530c64582c68ab530c09c3dae800cda043ba1f5468e81e","target":"record","created_at":"2026-05-18T01:00:40Z","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":"631b9c0b8ea9f5dcbed80d10103ce019cd0d7832ce22ea072167ff108f7fe6f4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-28T09:18:50Z","title_canon_sha256":"ce20481d0854aca4afd587e17311512fd34ac5f4f78264b00f09c03e4f3c4ed4"},"schema_version":"1.0","source":{"id":"1510.08231","kind":"arxiv","version":3}},"canonical_sha256":"d370a6abe2c20d935f1c03006d1fd93685531fe925aa0459cc1e355080def6cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d370a6abe2c20d935f1c03006d1fd93685531fe925aa0459cc1e355080def6cf","first_computed_at":"2026-05-18T01:00:40.260413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:40.260413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yJN5Dg/TE6dep3CoUdpxN8USG/zc/+SZvvzQGVDK35Jq5VoWcKlqs/UIbVy78vvVYz83Gt+W72Y7+Pd+/aQiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:40.261155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08231","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c4deed030b116cb3f530c64582c68ab530c09c3dae800cda043ba1f5468e81e","sha256:72410977bc0d855459eb4aeb39425f68c0eecb2bdfec84bfec58cb4dbd177ec6"],"state_sha256":"51626dfcd90128cadc238485dab37826e13254972305bb0a7ea7c9a68c6f6c38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vE/4u23AvebW4hGnWuieXF7bGDnlEoN2/oLedj6f4HLCc+q6gkOFZcEmb1gRFQwuYSJer0fNNj5kREjWDCJzAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:53:16.836226Z","bundle_sha256":"acdfdc2c8948400662f78e1d12bb9c08a33b8f4ddd07661ff223905515fe7a84"}}