{"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"}