Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning
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 ma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/5/825 |
| _version_ | 1827741420849463296 |
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| author | Naima Tasnim Jafar Mohammadi Anand D. Sarwate Hafiz Imtiaz |
| author_facet | Naima Tasnim Jafar Mohammadi Anand D. Sarwate Hafiz Imtiaz |
| author_sort | Naima Tasnim |
| collection | DOAJ |
| description | 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–utility 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–utility 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">CAPE</mi></semantics></math></inline-formula> protocol and propose <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">capeFM</mi></semantics></math></inline-formula>. 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. |
| first_indexed | 2024-03-11T03:46:18Z |
| format | Article |
| id | doaj.art-fdb1689d7e4245b398aae20dc3d36bd3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T03:46:18Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-fdb1689d7e4245b398aae20dc3d36bd32023-11-18T01:16:56ZengMDPI AGEntropy1099-43002023-05-0125582510.3390/e25050825Approximating Functions with Approximate Privacy for Applications in Signal Estimation and LearningNaima Tasnim0Jafar Mohammadi1Anand D. Sarwate2Hafiz Imtiaz3Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka P.O. Box 1205, BangladeshNokia, Werinherstraße 91, 81541 Munich, GermanyDepartment of Electrical and Computer Engineering, Rutgers, The State University of New Jersey, 94 Brett Road, Piscataway, NJ 08854-8058, USADepartment of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka P.O. Box 1205, BangladeshLarge 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–utility 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–utility 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">CAPE</mi></semantics></math></inline-formula> protocol and propose <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">capeFM</mi></semantics></math></inline-formula>. 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.https://www.mdpi.com/1099-4300/25/5/825differential privacyfunctional mechanismdecentralized-data systems |
| spellingShingle | Naima Tasnim Jafar Mohammadi Anand D. Sarwate Hafiz Imtiaz Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning Entropy differential privacy functional mechanism decentralized-data systems |
| title | Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning |
| title_full | Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning |
| title_fullStr | Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning |
| title_full_unstemmed | Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning |
| title_short | Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning |
| title_sort | approximating functions with approximate privacy for applications in signal estimation and learning |
| topic | differential privacy functional mechanism decentralized-data systems |
| url | https://www.mdpi.com/1099-4300/25/5/825 |
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