Fast and Robust Gaussian Process Inference for Bayesian Nonparametric Learning

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Advances in modern technology have empowered researchers to collect massive data to conduct inference and making predictions. With the abundance of available observations, traditional statistical methods under the parametric assumption that a model can be characterized by a pre-specified number of parameters become inadequate and less attractive. Bayesian nonparametric models are attractive in this context which allow the resolution level of the analysis to be determined in a data-driven manner, and provide automatic characterization of uncertainty. The goal of this project is to develop new theory, methodology and computational tools for Bayesian nonparametric inference via Gaussian process priors. Given the availability of massive data, nonparametric inference offers an attractive framework for flexibly modeling the underlying structure and extracting useful information. For instance, such challenges occur in chemical physics, computational biology, computer vision, engineering, and meteorology. This project aims to lay down a solid methodological, algorithmic, and theoretical foundation for nonparametric inference based on Gaussian processes. In particular, Gaussian process-based approaches tend to be vulnerable to data contamination and have heavy computational costs. To alleviate the high-computational cost of Gaussian process inference procedures, the investigator puts forward two novel computational frameworks which differ at their respective approximating targets as being either the prior or the posterior. To enhance the robustness of Gaussian process inference against data contamination, the investigator proposes a novel class of Bayesian hierarchical models for incorporating this extra measurement error structure, leading to a class of robust Gaussian process inference procedures. The new theoretical development offers valuable insight to experiment-design practitioners into the impact of measurement errors upon prediction and estimation, and provides evidence on the deep connection between computational complexity and statistical learnability. These computational and theoretical frameworks also benefit other disciplines such as applied mathematics, computer science and finance where stochastic processes such as Gaussian processes are routinely used. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.