{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ML7JCTWF2MWD5HB6JP6XBSYDEE","short_pith_number":"pith:ML7JCTWF","schema_version":"1.0","canonical_sha256":"62fe914ec5d32c3e9c3e4bfd70cb032139f4e41aebf492b00ba036469aa58d56","source":{"kind":"arxiv","id":"2502.20368","version":2},"attestation_state":"computed","paper":{"title":"Minimax rates for learning kernels in operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Fei Lu, Sichong Zhang, Xiong Wang","submitted_at":"2025-02-27T18:36:46Z","abstract_excerpt":"Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast to classical nonparametric regression, where the inverse problem is well-posed, kernel estimation involves a compact normal operator and an ill-posed deconvolution. To address these challenges, we introduce adaptive spectral Sobolev spaces, which unify Sobolev spaces and reproducing kernel Hilbert spaces, automatically discarding non-identifiable components"},"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":"2502.20368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-02-27T18:36:46Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"c20db343f55b4ac61fe00df17ca1dfa922010ef3df8bfd33f7079a030a5481cd","abstract_canon_sha256":"7abf8968912d35163a820540ddaa3a8c8ec124853bc55dcb8a777f801d961058"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:08.331372Z","signature_b64":"uCtfjbKtqrt03RgXLgFhsmoXhOWx/wn+Lq4TvzQcscYZIfj2dQlFHcjL2jCsx14c7i6omSdVMw4ULkIrw0RcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62fe914ec5d32c3e9c3e4bfd70cb032139f4e41aebf492b00ba036469aa58d56","last_reissued_at":"2026-07-05T11:25:08.330886Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:08.330886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimax rates for learning kernels in operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Fei Lu, Sichong Zhang, Xiong Wang","submitted_at":"2025-02-27T18:36:46Z","abstract_excerpt":"Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast to classical nonparametric regression, where the inverse problem is well-posed, kernel estimation involves a compact normal operator and an ill-posed deconvolution. To address these challenges, we introduce adaptive spectral Sobolev spaces, which unify Sobolev spaces and reproducing kernel Hilbert spaces, automatically discarding non-identifiable components"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20368","kind":"arxiv","version":2},"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/2502.20368/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.20368","created_at":"2026-07-05T11:25:08.330944+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.20368v2","created_at":"2026-07-05T11:25:08.330944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.20368","created_at":"2026-07-05T11:25:08.330944+00:00"},{"alias_kind":"pith_short_12","alias_value":"ML7JCTWF2MWD","created_at":"2026-07-05T11:25:08.330944+00:00"},{"alias_kind":"pith_short_16","alias_value":"ML7JCTWF2MWD5HB6","created_at":"2026-07-05T11:25:08.330944+00:00"},{"alias_kind":"pith_short_8","alias_value":"ML7JCTWF","created_at":"2026-07-05T11:25:08.330944+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.17672","citing_title":"When Rough Data Helps: A Phase Transition in Convergence Rates for Kernel Recovery in Integral Operators","ref_index":47,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11841","citing_title":"Minimax Rates and Spectral Distillation for Tree Ensembles","ref_index":79,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE","json":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE.json","graph_json":"https://pith.science/api/pith-number/ML7JCTWF2MWD5HB6JP6XBSYDEE/graph.json","events_json":"https://pith.science/api/pith-number/ML7JCTWF2MWD5HB6JP6XBSYDEE/events.json","paper":"https://pith.science/paper/ML7JCTWF"},"agent_actions":{"view_html":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE","download_json":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE.json","view_paper":"https://pith.science/paper/ML7JCTWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.20368&json=true","fetch_graph":"https://pith.science/api/pith-number/ML7JCTWF2MWD5HB6JP6XBSYDEE/graph.json","fetch_events":"https://pith.science/api/pith-number/ML7JCTWF2MWD5HB6JP6XBSYDEE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE/action/storage_attestation","attest_author":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE/action/author_attestation","sign_citation":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE/action/citation_signature","submit_replication":"https://pith.science/pith/ML7JCTWF2MWD5HB6JP6XBSYDEE/action/replication_record"}},"created_at":"2026-07-05T11:25:08.330944+00:00","updated_at":"2026-07-05T11:25:08.330944+00:00"}