{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/minimax-rates-of-estimating-approximate","title":"Minimax Rates of Estimating Approximate Differential Privacy","arxiv_id":"1905.10335","date":"2019-05-24","proceeding":null,"authors":["Xiyang Liu","Sewoong Oh"],"abstract":"Differential privacy has become a widely accepted notion of privacy, leading to the introduction and deployment of numerous privatization mechanisms. However, ensuring the privacy guarantee is an error-prone process, both in designing mechanisms and in implementing those mechanisms. Both types of errors will be greatly reduced, if we have a data-driven approach to verify privacy guarantees, from a black-box access to a mechanism. We pose it as a property estimation problem, and study the fundamental trade-offs involved in the accuracy in estimated privacy guarantees and the number of samples required. We introduce a novel estimator that uses polynomial approximation of a carefully chosen degree to optimally trade-off bias and variance. With $n$ samples, we show that this estimator achieves performance of a straightforward plug-in estimator with $n \\ln n$ samples, a phenomenon referred to as effective sample size amplification. The minimax optimality of the proposed estimator is proved by comparing it to a matching fundamental lower bound.","url_abs":"https://arxiv.org/abs/1905.10335v1","url_pdf":"https://arxiv.org/pdf/1905.10335v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"minimax-rates-of-estimating-approximate","repo_url":"https://github.com/OpenMined/PyDPValidator","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"minimax-rates-of-estimating-approximate","repo_url":"https://github.com/xiyangl3/adp-estimator","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1905.10335","atlas_url":"https://app.syntology.ai/?focus=1905.10335","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}