A Private and Computationally-Efficient Estimator for Unbounded Gaussians

Gautam Kamath; Argyris Mouzakis; Vikrant Singhal; Thomas Steinke; Jonathan Ullman

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arXiv · 2111.04609

A Private and Computationally-Efficient Estimator for Unbounded Gaussians

Gautam Kamath·Argyris Mouzakis·Vikrant Singhal·Thomas Steinke·Jonathan Ullman

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Abstract

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(μ,Σ)$ in $\mathbb{R}^d$. All previous estimators are either nonconstructive, with unbounded running time, or require the user to specify a priori bounds on the parameters $μ$ and $Σ$. The primary new technical tool in our algorithm is a new differentially private preconditioner that takes samples from an arbitrary Gaussian $\mathcal{N}(0,Σ)$ and returns a matrix $A$ such that $A ΣA^T$ has constant condition number.

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BibTeX RIS

Gautam Kamath, Argyris Mouzakis, Vikrant Singhal, Thomas Steinke, Jonathan Ullman. 2022-02-11. A Private and Computationally-Efficient Estimator for Unbounded Gaussians. https://arxiv.org/abs/2111.04609

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