{"paper":{"title":"Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew Stuart, Frank Pinski, Gideon Simpson, Hendrik Weber","submitted_at":"2013-10-29T15:35:59Z","abstract_excerpt":"In a variety of applications it is important to extract information from a probability measure $\\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time Markov processes. It may then be of interest to find a measure $\\nu$, from within a simple class of measures, which approximates $\\mu$. This problem is studied in the case where the Kullback-Leibler divergence is employed to measure the quality of the approximation. A calculus of variations viewpoint is adopted and the particular case where $\\nu$ is chosen from "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7845","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":""},"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"}