Shurong Lin

Shurong Lin, Aleksandra Slavković, Deekshith Reddy Bhoomireddy

In social sciences, small- to medium-scale datasets are common and linear regression (LR) is canonical. In privacy-aware settings, much work has focused on differentially private (DP) LR, but mostly on point estimation with limited attention to uncertainty quantification. Meanwhile, synthetic data generation (SDG) is increasingly important for reproducibility studies, yet current DP LR methods do not readily support it. Mainstream SDG approaches are either tailored to discretized data, making them less suitable for continuous regression, or rely on deep models that require large datasets, limiting their use for the smaller, continuous data typical in social science. We propose a method for LR with valid inference under Gaussian DP: a DP bias-corrected estimator with asymptotic confidence intervals (CIs) and a general SDG procedure in which regression on the synthetic data matches our DP regression. Our binning-aggregation strategy is effective in small- to moderate-dimensional settings. Experiments show our method (1) improves accuracy over existing methods, (2) provides valid CIs, and (3) produces more reliable synthetic data for downstream ML tasks than current DP SDGs.

Shurong Lin, Eric D. Kolaczyk, Adam Smith et al.

The interplay between optimization and privacy has become a central theme in privacy-preserving machine learning. Noisy stochastic gradient descent (SGD) has emerged as a cornerstone algorithm, particularly in large-scale settings. These variants of gradient methods inject carefully calibrated noise into each update to achieve differential privacy, the gold standard notion of rigorous privacy guarantees. Prior work primarily provides various bounds on statistical risk and privacy loss for noisy SGD, yet the \textit{exact} behavior of the process remains unclear, particularly in high-dimensional settings. This work leverages a diffusion approach to analyze noisy SGD precisely, providing a continuous-time perspective that captures both statistical risk evolution and privacy loss dynamics in high dimensions. Moreover, we study a variant of noisy SGD that does not require explicit knowledge of gradient sensitivity, unlike existing work that assumes or enforces sensitivity through gradient clipping. Specifically, we focus on the least squares problem with $\ell_2$ regularization.