{"paper":{"title":"How to implement the Bayes' formula in the age of ML?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Amirhossein Taghvaei, Prashant G. Mehta","submitted_at":"2024-11-14T18:21:05Z","abstract_excerpt":"This chapter contains a self-contained introduction to the significance of Bayes' formula in the context of nonlinear filtering problems. Both discrete-time and continuous-time settings of the problem are considered in a unified manner. In control theory, the focus on optimization-based solution approaches is stressed together with a discussion of historical developments in this area (from 1960s onwards). The heart of this chapter contains a presentation of a novel optimal transportation formulation for the Bayes formula (developed recently by the first author) and its relationship to some of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09653","kind":"arxiv","version":1},"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/2411.09653/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"}