Advancing High-Dimensional Bayesian Asymptotics and Computation

点击翻译按钮获取中文摘要

The big data revolution has turned statistics and machine learning into highly active and fast-pace research areas that have seen great progress over the last few decades. However uncertainly quantification with big data and complex models remains a challenge in the field. In theory, Bayesian statistics solves -- elegantly and straightforwardly -- the uncertainty quantification problem. There is therefore a need for ideas and methods for constructing useful and computationally scalable Bayesian procedures. This research project contributes towards that goal. The developed methodology can improve decision making in areas such as autonomous driving, medical diagnostics, bail decision, credit worthiness, criminal sentencing, to list a few. This research will also include training for graduate students. This project contributes to the development of theoretically sound, and computationally scalable Bayesian methodologies for the recovery of high-dimensional parameters. Toward that goal, the PI will develop a novel and widely applicable quasi-Bayesian (semi-parametric) framework for learning high-dimensional parameters. The project will also contribute to the development of Bayesian asymptotic theory with the analysis of high-dimensional, non-identifiable models. Several high-profile models (e.g. neural network models) widely used in the applications are non-identifiable. By applying the new framework to canonical correlation analysis, this project will also contribute to the development of flexible Bayesian solutions for high-dimensional sparse canonical correlation analysis, with wide applicability in bio-medical research. This research project will also contribute to the computational aspects of high-dimensional Bayesian statistics with the development of several novel MCMC and VA algorithms. Finally, this research project will also contribute more broadly to statistics and machine learning with the development of Bayesian generative adversarial networks (GAN).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.