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Near-Optimal differentially private low-rank trace regression with guaranteed private initialization
March 26, 2024, 4:43 a.m. | Mengyue Zha
cs.LG updates on arXiv.org arxiv.org
Abstract: We study differentially private (DP) estimation of a rank-$r$ matrix $M \in \RR^{d_1\times d_2}$ under the trace regression model with Gaussian measurement matrices. Theoretically, the sensitivity of non-private spectral initialization is precisely characterized, and the differential-privacy-constrained minimax lower bound for estimating $M$ under the Schatten-$q$ norm is established. Methodologically, the paper introduces a computationally efficient algorithm for DP-initialization with a sample size of $n \geq \wt O (r^2 (d_1\vee d_2))$. Under certain regularity conditions, the …
abstract arxiv cs.lg differential low matrix measurement minimax near privacy regression sensitivity stat.ml study type
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