{"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/convex-optimization-for-linear-query","title":"Convex Optimization for Linear Query Processing under Approximate Differential Privacy","arxiv_id":"1602.04302","date":"2016-02-13","proceeding":null,"authors":["Ganzhao Yuan","Yin Yang","Zhenjie Zhang","Zhifeng Hao"],"abstract":"Differential privacy enables organizations to collect accurate aggregates\nover sensitive data with strong, rigorous guarantees on individuals' privacy.\nPrevious work has found that under differential privacy, computing multiple\ncorrelated aggregates as a batch, using an appropriate \\emph{strategy}, may\nyield higher accuracy than computing each of them independently. However,\nfinding the best strategy that maximizes result accuracy is non-trivial, as it\ninvolves solving a complex constrained optimization program that appears to be\nnon-linear and non-convex. Hence, in the past much effort has been devoted in\nsolving this non-convex optimization program. Existing approaches include\nvarious sophisticated heuristics and expensive numerical solutions. None of\nthem, however, guarantees to find the optimal solution of this optimization\nproblem.\n  This paper points out that under ($\\epsilon$, $\\delta$)-differential privacy,\nthe optimal solution of the above constrained optimization problem in search of\na suitable strategy can be found, rather surprisingly, by solving a simple and\nelegant convex optimization program. Then, we propose an efficient algorithm\nbased on Newton's method, which we prove to always converge to the optimal\nsolution with linear global convergence rate and quadratic local convergence\nrate. Empirical evaluations demonstrate the accuracy and efficiency of the\nproposed solution.","url_abs":"http://arxiv.org/abs/1602.04302v3","url_pdf":"http://arxiv.org/pdf/1602.04302v3.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":"abstracts"},"code_links":[{"paper_slug":"convex-optimization-for-linear-query","repo_url":"https://github.com/cmla-psu/matrixqueries","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1602.04302","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}