A Private and Computationally-Efficient Estimator for Unbounded Gaussians

11/08/2021

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by   Gautam Kamath, et al.

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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.