{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:48:38Z","timestamp":1792792118939,"version":"4.5.0"},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. VLDB Endow."],"published-print":{"date-parts":[[2012,7]]},"abstract":"<jats:p>\n                    <jats:italic>\u03b5-differential privacy<\/jats:italic>\n                    is the state-of-the-art model for releasing sensitive information while protecting privacy. Numerous methods have been proposed to enforce \u03b5-differential privacy in various analytical tasks, e.g.,\n                    <jats:italic>regression analysis<\/jats:italic>\n                    . Existing solutions for regression analysis, however, are either limited to non-standard types of regression or unable to produce accurate regression results. Motivated by this, we propose the\n                    <jats:italic>Functional Mechanism<\/jats:italic>\n                    , a differentially private method designed for a large class of optimization-based analyses. The main idea is to enforce \u03b5-differential privacy by perturbing the\n                    <jats:italic>objective function<\/jats:italic>\n                    of the optimization problem, rather than its results. As case studies, we apply the functional mechanism to address two most widely used regression models, namely,\n                    <jats:italic>linear regression<\/jats:italic>\n                    and\n                    <jats:italic>logistic regression<\/jats:italic>\n                    . Both theoretical analysis and thorough experimental evaluations show that the functional mechanism is highly effective and efficient, and it significantly outperforms existing solutions.\n                  <\/jats:p>","DOI":"10.14778\/2350229.2350253","type":"journal-article","created":{"date-parts":[[2014,6,24]],"date-time":"2014-06-24T08:17:57Z","timestamp":1403597877000},"page":"1364-1375","source":"Crossref","is-referenced-by-count":268,"title":["Functional mechanism"],"prefix":"10.14778","volume":"5","author":[{"given":"Jun","family":"Zhang","sequence":"first","affiliation":[{"name":"Nanyang Technological University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenjie","family":"Zhang","sequence":"additional","affiliation":[{"name":"Advanced Digital Sciences Center, Illinois at Singapore Pte. Ltd."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaokui","family":"Xiao","sequence":"additional","affiliation":[{"name":"Nanyang Technological University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yin","family":"Yang","sequence":"additional","affiliation":[{"name":"Advanced Digital Sciences Center, Illinois at Singapore Pte. Ltd."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marianne","family":"Winslett","sequence":"additional","affiliation":[{"name":"Advanced Digital Sciences Center, Illinois at Singapore Pte. Ltd. and University of Illinois at Urbana-Champaign"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2012,7]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"T. Apostol. Calculus. Jon Wiley &amp; Sons 1967. T. Apostol. Calculus . 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Lei . Differentially private m-estimators . In Proceedings of the 23rd Annual Conference on Neural Information Processing Systems , 2011 . J. Lei. Differentially private m-estimators. In Proceedings of the 23rd Annual Conference on Neural Information Processing Systems, 2011."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1807085.1807104"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2046556.2046581"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1851182.1851199"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1557019.1557090"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2007.41"},{"key":"e_1_2_1_22_1","volume-title":"Integrated public use microdata series -- international: Version 5.0","author":"Minnesota Population Center","year":"2009","unstructured":"Minnesota Population Center . 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