On Differentially Private Mechanisms for Linear Regression

arXiv:2611.08737v1 Announce Type: new Abstract: We study the classic least-squares linear regression problem under differential privacy (DP) in the batch and the continual observation setting. In the latter setting, the mechanism receives a stream of $n$ data points $(x_i,y_i)$ ($x_i\in\mathbb{R}^d$ and $y_i\in\mathbb{R}$) and must output an estimate of the optimal parameters at each time step $i$. Although differentially private linear regression has been extensively studied in the batch setting, the problem remains underexplored for the continual setting, with prior work being restricted to constrained linear regression and update time polynomial in $n$.