A Private and Computationally-Efficient Estimator for Unbounded Gaussians [article]

Gautam Kamath, Argyris Mouzakis, Vikrant Singhal, Thomas Steinke, Jonathan Ullman
<span title="2022-02-11">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution 𝒩(μ,Σ) in 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 𝒩(0,Σ) and returns a matrix A such that A Σ A^T has constant condition number.
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