2022-06-28-kamath22a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
A Private and Computationally-Efficient Estimator for Unbounded Gaussians	We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $N(\mu,\Sigma)$ 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 $\mu$ and $\Sigma$. The primary new technical tool in our algorithm is a new differentially private preconditioner that takes samples from an arbitrary Gaussian $N(0,\Sigma)$ and returns a matrix $A$ such that $A \Sigma A^T$ has constant condition number	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	kamath22a	0	A Private and Computationally-Efficient Estimator for Unbounded Gaussians	544	572	544-572	544	false	Kamath, Gautam and Mouzakis, Argyris and Singhal, Vikrant and Steinke, Thomas and Ullman, Jonathan	given family Gautam Kamath given family Argyris Mouzakis given family Vikrant Singhal given family Thomas Steinke given family Jonathan Ullman	2022-06-28		Proceedings of Thirty Fifth Conference on Learning Theory	178	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v178/kamath22a/kamath22a.pdf