{"paper":{"title":"Bounding relative entropy by the relative entropy of local specifications in product spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Katalin Marton","submitted_at":"2009-07-26T15:48:45Z","abstract_excerpt":"For a class of density functions $q^n(x^n)$ on $\\Bbb R^n$ we prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: For any density function $p^n(x^n)$ on $\\Bbb R^n$, $D(p^n||q^n)\\leq Const. \\sum_{i=1}^n \\Bbb E D(p_i(\\cdot|Y_1,..., Y_{i-1},Y_{i+1},..., Y_n) || Q_i(\\cdot|Y_1,..., Y_{i-1},Y_{i+1},..., Y_n)),$ where $p_i(\\cdot|y_1,..., y_{i-1},y_{i+1},..., y_n)$ and $Q_i(\\cdot|x_1,..., x_{i-1},x_{i+1},..., x_n)$ denote the local specifications for $p^n$ resp. $q^n$, i.e., the conditional density functions of the $i$'th coordinate,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4491","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"}