{"paper":{"title":"PREM: Privately Answering Statistical Queries with Relative Error","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alexander Knop, Badih Ghazi, Crist\\'obal Guzm\\'an, Pasin Manurangsi, Pritish Kamath, Ravi Kumar, Sushant Sachdeva","submitted_at":"2025-02-20T18:32:02Z","abstract_excerpt":"We introduce $\\mathsf{PREM}$ (Private Relative Error Multiplicative weight update), a new framework for generating synthetic data that achieves a relative error guarantee for statistical queries under $(\\varepsilon, \\delta)$ differential privacy (DP). Namely, for a domain ${\\cal X}$, a family ${\\cal F}$ of queries $f : {\\cal X} \\to \\{0, 1\\}$, and $\\zeta > 0$, our framework yields a mechanism that on input dataset $D \\in {\\cal X}^n$ outputs a synthetic dataset $\\widehat{D} \\in {\\cal X}^n$ such that all statistical queries in ${\\cal F}$ on $D$, namely $\\sum_{x \\in D} f(x)$ for $f \\in {\\cal F}$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.14809","kind":"arxiv","version":1},"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/2502.14809/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"}