STA 701 Talk

Moderator: Patrick Woitschig

Speakers : Zeki Kazan and Rick Presman

Zeki Kazan

Bayesian Inference Under Differential Privacy: Prior Selection Considerations with Application to Univariate Gaussian Data and Regression" and the abstract is below.

We describe Bayesian inference for the mean and variance of bounded data protected by differential privacy and modeled as Gaussian. Using this setting, we demonstrate that analysts can and should take the constraints imposed by the bounds into account when specifying prior distributions. Additionally, we provide theoretical and empirical results regarding what classes of default priors produce valid inference for a differentially private release in settings where substantial prior information is not available. We discuss how these results can be applied to Bayesian inference for regression with differentially private data.

Rick Presman

Efficient Constrained Estimation via Projected Mirror Descent

Constraints on parameter spaces promote various structures in statistical and machine learning tasks. However, they present methodological and computational challenges. These challenges only become more evident in non-Euclidean settings. To address these challenges, we advocate for the use of the Projected Mirror Descent algorithm. In addition to asymptotic consistency, we show how this algorithm can under certain conditions produce asymptotically efficient estimators. Moreover, we connect Projected Mirror Descent to other algorithms of interest and demonstrate our theoretical analysis through various applications, highlighting ways this algorithm can be extended to a broad class of problems.