We study differentially private (DP) regression in settings where each data sample includes public, non-sensitive features\u2014common in applications like recommendation or advertising systems. While such label DP or DP with semi-sensitive features settings have been primarily explored in the context of classification, effective approaches for regression remain underexplored. We introduce \\(\\textsf{Cond-DP}\\), a conditioned variant of \\(\\textsf{DPSGD}\\) that leverages the structure of public feature matrices to improve optimization under privacy constraints. Motivated by the observation that these public features often exhibit rapidly decaying spectra, \\(\\textsf{Cond-DP}\\)\u00a0incorporates a data-driven conditioning matrix to reshape the optimization landscape and accelerate convergence. We provide convergence guarantees for convex, strongly convex and non-convex settings, and recover standard \\(\\textsf{DPSGD}\\)\u00a0as a special case when the conditioning matrix is the identity. We show how to construct an effective conditioning matrix for \\(\\textsf{Cond-DP}\\)\u00a0directly from public features, enabling faster convergence than \\(\\textsf{DPSGD}\\)\u00a0in private linear regression, without incurring additional privacy cost. Empirically, \\(\\textsf{Cond-DP}\\)\u00a0with this conditioning matrix consistently outperforms state-of-the-art baselines across a wide range of datasets and model architectures under label DP, demonstrating strong and robust performance in practice.<\/p>\n","protected":false},"excerpt":{"rendered":"
We study differentially private (DP) regression in settings where each data sample includes public, non-sensitive features\u2014common in applications like recommendation or advertising systems. While such label DP or DP with semi-sensitive features settings have been primarily explored in the context of classification, effective approaches for regression remain underexplored. 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