{"paper":{"title":"On Pinsker's Type Inequalities and Csiszar's f-divergences. Part I: Second and Fourth-Order Inequalities","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gustavo L. Gilardoni","submitted_at":"2006-03-24T11:47:59Z","abstract_excerpt":"We study conditions on $f$ under which an $f$-divergence $D_f$ will satisfy $D_f \\geq c_f V^2$ or $D_f \\geq c_{2,f} V^2 + c_{4,f} V^4$, where $V$ denotes variational distance and the coefficients $c_f$, $c_{2,f}$ and $c_{4,f}$ are {\\em best possible}. As a consequence, we obtain lower bounds in terms of $V$ for many well known distance and divergence measures. For instance, let $D_{(\\alpha)} (P,Q) = [\\alpha (\\alpha-1)]^{-1} [\\int q^{\\alpha} p^{1-\\alpha} d \\mu -1]$ and ${\\cal I}_\\alpha (P,Q) = (\\alpha -1)^{-1} \\log [\\int p^\\alpha q^{1-\\alpha} d \\mu]$ be respectively the {\\em relative informatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0603097","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"}