2023
Journal articles
- titre
- On the Statistical Complexity of Estimation and Testing under Privacy Constraints
- auteur
- Clément Lalanne, Aurélien Garivier, Rémi Gribonval
- article
- Transactions on Machine Learning Research Journal, 2023
- resume
- The challenge of producing accurate statistics while respecting the privacy of the individuals in a sample is an important area of research. We study minimax lower bounds for classes of differentially private estimators. In particular, we show how to characterize the power of a statistical test under differential privacy in a plug-and-play fashion by solving an appropriate transport problem. With specific coupling constructions, this observation allows us to derive Le Cam-type and Fano-type inequalities not only for regular definitions of differential privacy but also for those based on Renyi divergence. We then proceed to illustrate our results on three simple, fully worked out examples. In particular, we show that the problem class has a huge importance on the provable degradation of utility due to privacy. In certain scenarios, we show that maintaining privacy results in a noticeable reduction in performance only when the level of privacy protection is very high. Conversely, for other problems, even a modest level of privacy protection can lead to a significant decrease in performance. Finally, we demonstrate that the DP-SGLD algorithm, a private convex solver, can be employed for maximum likelihood estimation with a high degree of confidence, as it provides near-optimal results with respect to both the size of the sample and the level of privacy protection. This algorithm is applicable to a broad range of parametric estimation procedures, including exponential families.
- Accès au texte intégral et bibtex
-
Conference papers
- titre
- Private Statistical Estimation of Many Quantiles
- auteur
- Clément Lalanne, Aurélien Garivier, Rémi Gribonval
- article
- ICML 2023 - 40th International Conference on Machine Learning, Jul 2023, Honolulu, United States
- resume
- This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution function (the quantile function) at specific points. For instance, this task is of key importance in private data generation. We present two different approaches. The first one consists in privately estimating the empirical quantiles of the samples and using this result as an estimator of the quantiles of the distribution. In particular, we study the statistical properties of the recently published algorithm introduced by Kaplan et al. 2022 that privately estimates the quantiles recursively. The second approach is to use techniques of density estimation in order to uniformly estimate the quantile function on an interval. In particular, we show that there is a tradeoff between the two methods. When we want to estimate many quantiles, it is better to estimate the density rather than estimating the quantile function at specific points.
- Accès au texte intégral et bibtex
-
Preprints, Working Papers, ...
- titre
- Sparsity in neural networks can improve their privacy
- auteur
- Antoine Gonon, Léon Zheng, Clément Lalanne, Quoc-Tung Le, Guillaume Lauga, Can Pouliquen
- article
- 2023
- resume
- This article measures how sparsity can make neural networks more robust to membership inference attacks. The obtained empirical results show that sparsity improves the privacy of the network, while preserving comparable performances on the task at hand. This empirical study completes and extends existing literature.
- Accès au texte intégral et bibtex
-
- titre
- Private Quantiles Estimation in the Presence of Atoms
- auteur
- Clément Sébastien Lalanne, Clément Gastaud, Nicolas Grislain, Aurélien Garivier, Rémi Gribonval
- article
- 2023
- resume
- We consider the differentially private estimation of multiple quantiles (MQ) of a distribution from a dataset, a key building block in modern data analysis. We apply the recent non-smoothed Inverse Sensitivity (IS) mechanism to this specific problem. We establish that the resulting method is closely related to the recently published ad hoc algorithm JointExp. In particular, they share the same computational complexity and a similar efficiency. We prove the statistical consistency of these two algorithms for continuous distributions. Furthermore, we demonstrate both theoretically and empirically that this method suffers from an important lack of performance in the case of peaked distributions, which can degrade up to a potentially catastrophic impact in the presence of atoms. Its smoothed version (i.e. by applying a max kernel to its output density) would solve this problem, but remains an open challenge to implement. As a proxy, we propose a simple and numerically efficient method called Heuristically Smoothed JointExp (HSJointExp), which is endowed with performance guarantees for a broad class of distributions and achieves results that are orders of magnitude better on problematic datasets.
- Accès au texte intégral et bibtex
-
2020
Conference papers
- titre
- Extraction of Nystagmus Patterns from Eye-Tracker Data with Convolutional Sparse Coding
- auteur
- Clément Lalanne, Maxence Rateaux, Laurent Oudre, Matthieu P Robert, Thomas Moreau
- article
- EMBC 2020 - 42nd Annual International Conferences of the IEEE Engineering in Medicine and Biology Society in conjunction with the 43rd Annual Conference of the Canadian Medical and Biological Engineering Society, Jul 2020, Montreal / Virtuel, Canada. pp.928-931
- resume
- The analysis of the Nystagmus waveforms from eye-tracking records is crucial for the clinicial interpretation of this pathological movement. A major issue to automatize this analysis is the presence of natural eye movements and eye blink artefacts that are mixed with the signal of interest. We propose a method based on Convolutional Dictionary Learning that is able to automaticcaly highlight the Nystagmus waveforms, separating the natural motion from the pathological movements. We show on simulated signals that our method can indeed improve the pattern recovery rate and provide clinical examples to illustrate how this algorithm performs.
- Accès au texte intégral et bibtex
-