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Gaussian DP for Reporting Differential Privacy Guarantees in Machine Learning

Year: 2025
Type: preprint
Abstract: Current practices for reporting differential privacy (DP) guarantees for machine learning (ML) algorithms such as DP-SGD provide an incomplete and potentially misleading picture. For instance, if only a single $(\varepsilon, δ)$ is known about a mechanism, standard analyses show that there could exist highly accurate inference attacks against training data records, when, upon a more careful analysis, such accurate attacks do not exist for most practical mechanisms. In this position paper, we argue that using _non-asymptotic_ Gaussian Differential Privacy (GDP) as the primary means of communicating DP guarantees in ML avoids these potential downsides. Using two recent developments in the DP literature: (i) open-source numerical accountants capable of computing the privacy profile and $f$-DP curves of DP-SGD to arbitrary accuracy, and (ii) a decision-theoretic metric over DP representations, we show how to provide non-asymptotic bounds on GDP using numerical accountants, and show that GDP can capture the entire privacy profile of DP-SGD and related algorithms with virtually no error, as quantified by the metric. To support our claims, we investigate the privacy profiles of state-of-the-art DP large-scale image classification, and the TopDown algorithm for the U.S. Decennial Census, observing that GDP fits their profiles remarkably well in all cases. We conclude with a discussion on the strengths and weaknesses of this approach, and discuss which other privacy mechanisms could benefit from GDP.
DOI: 10.48550/arxiv.2503.10945
Authors: Gomez, Juan Felipe, Kulynych, Bogdan, Kaissis, Georgios, Calmon, Flavio P., Hayes, Jamie, Balle, Borja, Honkela, Antti
Language: English
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, European Commission, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Finnish Center for Artificial Intelligence, Office of Science, Strategic Research Council, Advanced Scientific Computing Research
Awards: 2021 BUDGET REQUEST FOR THE DOE COMPUTATIONAL SCIENCE GRADUATE FELLOWSHIP (CSGF) GRANT, Synthetic Data Generation Framework for Integrated Validation of Use Cases and AI Healthcare Applications, G2900401177, European Lighthouse on Secure and Safe AI, 2021 BUDGET REQUEST FOR THE DOE COMPUTATIONAL SCIENCE GRADUATE FELLOWSHIP (CSGF) GRANT, Bridging Regulatory Data Protection Standards and Model Sharing in Healthcare, G7961519653, Medical, Multilingual and Privacy-Preserving Natural Language Processing in the Clinical Domain
OpenAlex ID: W4414812185
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