{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:09:12Z","timestamp":1774631352145,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T00:00:00Z","timestamp":1684713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["CNS-2148104"],"award-info":[{"award-number":["CNS-2148104"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["CIF-1453432"],"award-info":[{"award-number":["CIF-1453432"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"publisher","award":["2R01DA040487-01A1"],"award-info":[{"award-number":["2R01DA040487-01A1"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"US National Institutes of Health","doi-asserted-by":"publisher","award":["CNS-2148104"],"award-info":[{"award-number":["CNS-2148104"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"US National Institutes of Health","doi-asserted-by":"publisher","award":["CIF-1453432"],"award-info":[{"award-number":["CIF-1453432"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"US National Institutes of Health","doi-asserted-by":"publisher","award":["2R01DA040487-01A1"],"award-info":[{"award-number":["2R01DA040487-01A1"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Large corporations, government entities and institutions such as hospitals and census bureaus routinely collect our personal and sensitive information for providing services. A key technological challenge is designing algorithms for these services that provide useful results, while simultaneously maintaining the privacy of the individuals whose data are being shared. Differential privacy (DP) is a cryptographically motivated and mathematically rigorous approach for addressing this challenge. Under DP, a randomized algorithm provides privacy guarantees by approximating the desired functionality, leading to a privacy\u2013utility trade-off. Strong (pure DP) privacy guarantees are often costly in terms of utility. Motivated by the need for a more efficient mechanism with better privacy\u2013utility trade-off, we propose Gaussian FM, an improvement to the functional mechanism (FM) that offers higher utility at the expense of a weakened (approximate) DP guarantee. We analytically show that the proposed Gaussian FM algorithm can offer orders of magnitude smaller noise compared to the existing FM algorithms. We further extend our Gaussian FM algorithm to decentralized-data settings by incorporating the CAPE protocol and propose capeFM. Our method can offer the same level of utility as its centralized counterparts for a range of parameter choices. We empirically show that our proposed algorithms outperform existing state-of-the-art approaches on synthetic and real datasets.<\/jats:p>","DOI":"10.3390\/e25050825","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T02:28:42Z","timestamp":1684722522000},"page":"825","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-3404-0956","authenticated-orcid":false,"given":"Naima","family":"Tasnim","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka P.O. Box 1205, Bangladesh"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7141-2107","authenticated-orcid":false,"given":"Jafar","family":"Mohammadi","sequence":"additional","affiliation":[{"name":"Nokia, Werinherstra\u00dfe 91, 81541 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6123-5282","authenticated-orcid":false,"given":"Anand D.","family":"Sarwate","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Rutgers, The State University of New Jersey, 94 Brett Road, Piscataway, NJ 08854-8058, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2042-5941","authenticated-orcid":false,"given":"Hafiz","family":"Imtiaz","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka P.O. Box 1205, Bangladesh"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Differential Privacy","volume":"Volume 4052","author":"Dwork","year":"2006","journal-title":"Automata, Languages and Programming. ICALP 2006"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/MSP.2013.2259911","article-title":"Signal processing and machine learning with differential privacy: Algorithms and challenges for continuous data","volume":"30","author":"Sarwate","year":"2013","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","unstructured":"Jayaraman, B., and Evans, D. (2019, January 14\u201316). Evaluating differentially private machine learning in practice. Proceedings of the 28th USENIX Security Symposium (USENIX Security 19), Santa Clara, CA, USA."},{"key":"ref_4","unstructured":"Dwork, C., McSherry, F., Nissim, K., and Smith, A. 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