Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares
arxiv(2024)
摘要
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^⊤ 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 build on the
approach of Brown et al. (2023) for private mean estimation, adding scaled
noise to a carefully designed stable nonprivate estimator of the empirical
regression vector.
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