Flexible modeling and estimation for high-dimensional graphs

Abstract

With the wealth of large-scale data arising from biology, the Internet, and social science, there is a growing need for exploratory tools for data analysis. It is often of interest to estimate the underlying graph of the variables. This dissertation focuses on developing flexible statistical models for complex graphs motivated by scientific questions in genome science and neuroscience. We investigate three types of graphical models: mixed graphical models, systems of additive ordinary differential equations, and multivariate Hawkes processes. For each type of graphical models, we discuss the properties of the graphical model and propose efficient statistical methods for recovering the graphical structure from high-dimensional data. Furthermore, we establish statistical guarantees of the proposed procedures and conduct extensive numerical experiments to evaluate their empirical performance.