{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2NYKNK7CYIGZGXY4AMAG2H6ZG2","short_pith_number":"pith:2NYKNK7C","schema_version":"1.0","canonical_sha256":"d370a6abe2c20d935f1c03006d1fd93685531fe925aa0459cc1e355080def6cf","source":{"kind":"arxiv","id":"1510.08231","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.08231","created_at":"2026-05-18T01:00:40.260526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.08231v3","created_at":"2026-05-18T01:00:40.260526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08231","created_at":"2026-05-18T01:00:40.260526+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NYKNK7CYIGZ","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NYKNK7CYIGZGXY4","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NYKNK7C","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2","json":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2.json","graph_json":"https://pith.science/api/pith-number/2NYKNK7CYIGZGXY4AMAG2H6ZG2/graph.json","events_json":"https://pith.science/api/pith-number/2NYKNK7CYIGZGXY4AMAG2H6ZG2/events.json","paper":"https://pith.science/paper/2NYKNK7C"},"agent_actions":{"view_html":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2","download_json":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2.json","view_paper":"https://pith.science/paper/2NYKNK7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.08231&json=true","fetch_graph":"https://pith.science/api/pith-number/2NYKNK7CYIGZGXY4AMAG2H6ZG2/graph.json","fetch_events":"https://pith.science/api/pith-number/2NYKNK7CYIGZGXY4AMAG2H6ZG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/action/storage_attestation","attest_author":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/action/author_attestation","sign_citation":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/action/citation_signature","submit_replication":"https://pith.science/pith/2NYKNK7CYIGZGXY4AMAG2H6ZG2/action/replication_record"}},"created_at":"2026-05-18T01:00:40.260526+00:00","updated_at":"2026-05-18T01:00:40.260526+00:00"}