{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CU3NGNCZNGOLLW7CPFH6467VRU","short_pith_number":"pith:CU3NGNCZ","schema_version":"1.0","canonical_sha256":"1536d33459699cb5dbe2794fee7bf58d1f063a633e578967385e5f85a196661c","source":{"kind":"arxiv","id":"1410.6847","version":4},"attestation_state":"computed","paper":{"title":"Regularized Learning Schemes in Feature Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Patrick L. Combettes, Saverio Salzo, Silvia Villa","submitted_at":"2014-10-24T22:19:39Z","abstract_excerpt":"This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with totally convex functions. This broad class of regularizers provides a flexible model for various priors on the features, including in particular hard constraints and powers of Banach norms. In such context, the main results establish a new general form of the representer theorem and the consistency of the corresponding learning schemes under general conditions on "},"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":"1410.6847","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-10-24T22:19:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d964ea05baf643df1122941c8db413d70218d51a51600a75455ea153e44297be","abstract_canon_sha256":"4448cae8b61419b8016d0d3bd53f58942894ea4cdde13cc3fc7cd95582adb761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:52.511667Z","signature_b64":"mZJuATmQnmYYZ92clpWH+4cu1uEIGUTnVshxrKEUs/bIDkpZ/DchU/3nSqp8iCN4YaCAbcxJjkBOmoDP+gS9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1536d33459699cb5dbe2794fee7bf58d1f063a633e578967385e5f85a196661c","last_reissued_at":"2026-05-18T01:01:52.510931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:52.510931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularized Learning Schemes in Feature Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Patrick L. Combettes, Saverio Salzo, Silvia Villa","submitted_at":"2014-10-24T22:19:39Z","abstract_excerpt":"This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with totally convex functions. This broad class of regularizers provides a flexible model for various priors on the features, including in particular hard constraints and powers of Banach norms. In such context, the main results establish a new general form of the representer theorem and the consistency of the corresponding learning schemes under general conditions on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6847","kind":"arxiv","version":4},"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":"1410.6847","created_at":"2026-05-18T01:01:52.511045+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6847v4","created_at":"2026-05-18T01:01:52.511045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6847","created_at":"2026-05-18T01:01:52.511045+00:00"},{"alias_kind":"pith_short_12","alias_value":"CU3NGNCZNGOL","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"CU3NGNCZNGOLLW7C","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"CU3NGNCZ","created_at":"2026-05-18T12:28:25.294606+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/CU3NGNCZNGOLLW7CPFH6467VRU","json":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU.json","graph_json":"https://pith.science/api/pith-number/CU3NGNCZNGOLLW7CPFH6467VRU/graph.json","events_json":"https://pith.science/api/pith-number/CU3NGNCZNGOLLW7CPFH6467VRU/events.json","paper":"https://pith.science/paper/CU3NGNCZ"},"agent_actions":{"view_html":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU","download_json":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU.json","view_paper":"https://pith.science/paper/CU3NGNCZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6847&json=true","fetch_graph":"https://pith.science/api/pith-number/CU3NGNCZNGOLLW7CPFH6467VRU/graph.json","fetch_events":"https://pith.science/api/pith-number/CU3NGNCZNGOLLW7CPFH6467VRU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU/action/storage_attestation","attest_author":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU/action/author_attestation","sign_citation":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU/action/citation_signature","submit_replication":"https://pith.science/pith/CU3NGNCZNGOLLW7CPFH6467VRU/action/replication_record"}},"created_at":"2026-05-18T01:01:52.511045+00:00","updated_at":"2026-05-18T01:01:52.511045+00:00"}