all AI news
Covariance-Aware Private Mean Estimation Without Private Covariance Estimation
March 27, 2024, 4:43 a.m. | Gavin Brown, Marco Gaboardi, Adam Smith, Jonathan Ullman, Lydia Zakynthinou
cs.LG updates on arXiv.org arxiv.org
Abstract: We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \gtrsim d/\alpha^2$ samples from such a distribution with mean $\mu$ and covariance $\Sigma$, our estimators output $\tilde\mu$ such that $\| \tilde\mu - \mu \|_{\Sigma} \leq \alpha$, where $\| \cdot \|_{\Sigma}$ is the Mahalanobis distance. All previous estimators with the same guarantee either require strong a priori bounds on the covariance matrix or require $\Omega(d^{3/2})$ samples.
Each of …
abstract alpha arxiv covariance cs.lg distribution mean sample samples type
More from arxiv.org / cs.LG updates on arXiv.org
Jobs in AI, ML, Big Data
Artificial Intelligence – Bioinformatic Expert
@ University of Texas Medical Branch | Galveston, TX
Lead Developer (AI)
@ Cere Network | San Francisco, US
Research Engineer
@ Allora Labs | Remote
Ecosystem Manager
@ Allora Labs | Remote
Founding AI Engineer, Agents
@ Occam AI | New York
AI Engineer Intern, Agents
@ Occam AI | US