We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions. First, we show that robust statistics can be used in conjunction with noisy gradient descent or noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively. We establish local and global convergence guarantees, under both local strong convexity and self-concordance, showing that our private estimators converge with high probability to a small neighborhood of the nonprivate M-estimators. Second, we tackle the problem of parametric inference by constructing differentially private estimators of the asymptotic variance of our private M-estimators. This naturally leads to approximate pivotal statistics for constructing confidence regions and conducting hypothesis testing. We demonstrate the effectiveness of a bias correction that leads to enhanced small-sample empirical performance in simulations. We illustrate the benefits of our methods in several numerical examples.

Marco Avella-Medina

Casey Bradshaw

Po-Ling Loh

The Annals of Statistics

《统计年鉴》旨在发表反映当代统计诸多方面的最高质量研究论文。主要强调重要性和独创性，而不是形式主义。该杂志旨在涵盖统计学的所有领域，尤其是数理统计学和应用与跨学科统计学。当然，许多最好的论文将涉及不止一个这些一般领域，因为统计学科深深植根于数学和实质性科学领域。

The Annals of Statistics aims to publish high-quality research papers that reflect various aspects of contemporary statistics. The journal emphasizes the importance and originality of the research rather than formalism. It covers all areas of statistics, particularly mathematical statistics and applied and interdisciplinary statistics. Many of the best papers will involve more than one of these general areas, as the field of statistics is deeply rooted in mathematics and substantive sciences.

《Annals of Statistics》旨在发表反映当代统计学各个方面的高质量研究论文。该期刊主要强调研究的重要性和独创性，而非形式主义。它涵盖统计学的所有领域，特别是数理统计和应用统计及跨学科统计。许多优秀的论文往往涉及多个领域，因为统计学与数学及其他实质性科学领域密切相关。

Annals of Statistics

Ann. Statist.

Differentially private inference via noisy optimization

This work shows that robust statistics can be used in conjunction with noisy gradient descent or noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively, and establishes local and global convergence guarantees.

Category	Quartile
数学	1
数学, 统计学与概率论	1

Differentially private inference via noisy optimization

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	1