{"paper":{"title":"Private Algorithms Can Always Be Extended","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DS","stat.TH"],"primary_cat":"math.ST","authors_text":"Adam Smith, Christian Borgs, Ilias Zadik, Jennifer Chayes","submitted_at":"2018-10-30T04:12:13Z","abstract_excerpt":"We consider the following fundamental question on $\\epsilon$-differential privacy. Consider an arbitrary $\\epsilon$-differentially private algorithm defined on a subset of the input space. Is it possible to extend it to an $\\epsilon'$-differentially private algorithm on the whole input space for some $\\epsilon'$ comparable with $\\epsilon$? In this note we answer affirmatively this question for $\\epsilon'=2\\epsilon$. Our result applies to every input metric space and space of possible outputs. This result originally appeared in a recent paper by the authors [BCSZ18]. We present a self-contained"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12518","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"}