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Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares
April 25, 2024, 7:11 p.m. | Gavin Brown, Jonathan Hayase, Samuel Hopkins, Weihao Kong, Xiyang Liu, Sewoong Oh, Juan C. Perdomo, Adam Smith
cs.CR updates on arXiv.org arxiv.org
Abstract: We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix. All prior private algorithms for this task require either $d^{3/2}$ examples, error growing polynomially with the condition number, or exponential time. Our near-optimal accuracy guarantee holds for any dataset with bounded statistical leverage and bounded residuals. Technically, we …
algorithm algorithms arxiv cs.cr cs.lg design error matrix private sample statistics stat.ml task
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