Differentially Private Inference for Longitudinal Linear Regression

Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing methods almost exclusively address the item-level DP setting, where each user contributes a single observation. Many scientific and economic applications instead involve longitudinal or panel data, in which each user contributes multiple dependent observations. In these settings, item-level DP offers inadequate protection, and user-level DP - shielding an individual's entire trajectory - is the appropriate privacy notion. We develop a comprehensive framework for estimation and inference in longitudinal linear regression under user-level DP. We propose a user-level private regression estimator based on aggregating local regressions, and we establish finite-sample guarantees and asymptotic normality under short-range dependence. For inference, we develop a privatized, bias-corrected covariance estimator that is automatically heteroskedasticity- and autocorrelation-consistent. These results provide the first unified framework for practical user-level DP estimation and inference in longitudinal linear regression under dependence, with strong theoretical guarantees and promising empirical performance.

Scalable Differentially Private Bayesian Optimization

In recent years, there has been much work on scaling Bayesian Optimization to high-dimensional problems, for example hyperparameter tuning in large neural network models. These scalable methods have been successful, finding high objective values much more quickly than traditional global Bayesian Optimization or random search-based methods. At the same time, these large neural network models often use sensitive data, but preservation of Differential Privacy has not scaled alongside these modern Bayesian Optimization procedures. Here we develop a method to privately estimate potentially high-dimensional parameter spaces using Gradient Informative Bayesian Optimization. Our theoretical results prove that under suitable conditions, our method converges exponentially fast to a ball around the optimal parameter configuration. Moreover, regardless of whether the assumptions are satisfied, we show that our algorithm maintains privacy and empirically demonstrates superior performance to existing methods in the high-dimensional hyperparameter setting.