{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FLZ37CW75QKQEJPRPW3TRWQLVV","short_pith_number":"pith:FLZ37CW7","schema_version":"1.0","canonical_sha256":"2af3bf8adfec150225f17db738da0bad72f4785409e7044f1c2145123754f77f","source":{"kind":"arxiv","id":"2412.00412","version":3},"attestation_state":"computed","paper":{"title":"Functional worst risk minimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Ernst C. Wit, Philip Kennerberg","submitted_at":"2024-11-30T09:39:32Z","abstract_excerpt":"The aim of this paper is to extend worst risk minimization, also called worst average loss minimization, to the functional realm. This means finding a functional regression representation that will be robust to future distribution shifts on the basis of data from two environments. In the classical non-functional realm, structural equations are based on a transfer matrix $B$. In section~\\ref{sec:sfr}, we generalize this to consider a linear operator $\\mathcal{T}$ on square integrable processes that plays the the part of $B$. By requiring that $(I-\\mathcal{T})^{-1}$ is bounded -- as opposed to $"},"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":"2412.00412","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-11-30T09:39:32Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"0c36162107e2e6eb1e50751b715ac01bdd5faef3bceb8bc9f7f50adf09048777","abstract_canon_sha256":"1deb9b1368400f80cf420bd4ae537df03cac15e70478eee1b9ba174f09fee766"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:57.544500Z","signature_b64":"+EQeKRrPezSb4tn6tagRebfp2HSmT7nZTl91Gf9sRZvAE+ZW4/h1D2K0Vz9DSWEvU177FBlnHhJGOS2KbO82AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2af3bf8adfec150225f17db738da0bad72f4785409e7044f1c2145123754f77f","last_reissued_at":"2026-07-05T10:48:57.544006Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:57.544006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional worst risk minimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Ernst C. Wit, Philip Kennerberg","submitted_at":"2024-11-30T09:39:32Z","abstract_excerpt":"The aim of this paper is to extend worst risk minimization, also called worst average loss minimization, to the functional realm. This means finding a functional regression representation that will be robust to future distribution shifts on the basis of data from two environments. In the classical non-functional realm, structural equations are based on a transfer matrix $B$. In section~\\ref{sec:sfr}, we generalize this to consider a linear operator $\\mathcal{T}$ on square integrable processes that plays the the part of $B$. By requiring that $(I-\\mathcal{T})^{-1}$ is bounded -- as opposed to $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00412","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.00412/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":"2412.00412","created_at":"2026-07-05T10:48:57.544060+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.00412v3","created_at":"2026-07-05T10:48:57.544060+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.00412","created_at":"2026-07-05T10:48:57.544060+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLZ37CW75QKQ","created_at":"2026-07-05T10:48:57.544060+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLZ37CW75QKQEJPR","created_at":"2026-07-05T10:48:57.544060+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLZ37CW7","created_at":"2026-07-05T10:48:57.544060+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/FLZ37CW75QKQEJPRPW3TRWQLVV","json":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV.json","graph_json":"https://pith.science/api/pith-number/FLZ37CW75QKQEJPRPW3TRWQLVV/graph.json","events_json":"https://pith.science/api/pith-number/FLZ37CW75QKQEJPRPW3TRWQLVV/events.json","paper":"https://pith.science/paper/FLZ37CW7"},"agent_actions":{"view_html":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV","download_json":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV.json","view_paper":"https://pith.science/paper/FLZ37CW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.00412&json=true","fetch_graph":"https://pith.science/api/pith-number/FLZ37CW75QKQEJPRPW3TRWQLVV/graph.json","fetch_events":"https://pith.science/api/pith-number/FLZ37CW75QKQEJPRPW3TRWQLVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV/action/storage_attestation","attest_author":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV/action/author_attestation","sign_citation":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV/action/citation_signature","submit_replication":"https://pith.science/pith/FLZ37CW75QKQEJPRPW3TRWQLVV/action/replication_record"}},"created_at":"2026-07-05T10:48:57.544060+00:00","updated_at":"2026-07-05T10:48:57.544060+00:00"}