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arXiv · 1805.00216

Privately Learning High-Dimensional Distributions

Gautam Kamath·Jerry Li·Vikrant Singhal·Jonathan Ullman
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Abstract

We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in total variation distance. The sample complexity of our algorithms nearly matches the sample complexity of the optimal non-private learners for these tasks in a wide range of parameters, showing that privacy comes essentially for free for these problems. In particular, in contrast to previous approaches, our algorithm for learning Gaussians does not require strong a priori bounds on the range of the parameters. Our algorithms introduce a novel technical approach to reducing the sensitivity of the estimation procedure that we call recursive private preconditioning.

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BibTeXRIS

Gautam Kamath, Jerry Li, Vikrant Singhal, Jonathan Ullman. 2018-05-01. Privately Learning High-Dimensional Distributions. https://arxiv.org/abs/1805.00216

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