Reducing the Price of Uncertainty: Scalable Computational Approaches for High-Dimensional Probabilistic Modeling

Abstract

Probabilistic models provide a principled way to model observed data, perform statistical inferences, and express uncertainty over latent variables. However, it remains computationally challenging to fit high-dimensional probabilistic models to data. In this dissertation, we provide a suite of approaches for reducing this computational burden for various probabilistic models of interest. We examine models along the entire spectrum of structured to flexible, tackling diverse examples such as sparse Bayesian learning, latent Gaussian models, log-concave densities, and mixture models. Our methodologies are a rich combination of mathematical developments that leverage tools spanning optimization and statistics, as well as computational advances such as parallel computing and automatic differentiation.