{"paper":{"title":"Contraction of $E_\\gamma$-Divergence and Its Applications to Privacy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","cs.LG","math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Flavio P. Calmon, Mario Diaz, Shahab Asoodeh","submitted_at":"2020-12-20T22:02:15Z","abstract_excerpt":"We investigate the contraction coefficients derived from strong data processing inequalities for the $E_\\gamma$-divergence. By generalizing the celebrated Dobrushin's coefficient from total variation distance to $E_\\gamma$-divergence, we derive a closed-form expression for the contraction of $E_\\gamma$-divergence. This result has fundamental consequences in two privacy settings. First, it implies that local differential privacy can be equivalently expressed in terms of the contraction of $E_\\gamma$-divergence. This equivalent formula can be used to precisely quantify the impact of local privac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11035","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.11035/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"}