New advances in structure learning of graphical models
Restricted (Penn State Only)
- Author:
- Tao, Jun
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 03, 2022
- Committee Members:
- Ephraim Mont Hanks, Professor in Charge/Director of Graduate Studies
Lingzhou Xue, Chair & Dissertation Advisor
Antonio Blanca, Outside Unit & Field Member
Bing Li, Dissertation Co-Advisor
Runze Li, Major Field Member - Keywords:
- graphical model
statistical learning - Abstract:
- Graphical modeling of multivariate data is drawing increasing attention in theoretical and applied statistics. It is powerful due to its effective representation of high-dimensional data, making the structure more intuitive and easier to understand. Over the past decades, graphical models have been proposed for various fields of study. In this dissertation, we study statistical graphical models to handle different types of data. In particular, we propose three new graphical models: (1) an additive semi-graphoid model for discrete data, (2) a time-varying transnormal model for non-Gaussian data, and (3) a graphical temporal point process model for event stream data, especially for the path to purchase data in multi-touch attribution. Methodologically, we provide new tools to represent statistical relations between variables. The additive semi-graphoid model for discrete data focuses on additive conditional independence. The time-varying transnormal model explores the dynamic pattern of conditional independence. The graphical temporal point process model for event stream data aims at revealing the Granger causality between events in longitudinal order. We also develop learning methods for the new graphical models via the penalized estimation and establish the consistency of the estimators under the high-dimensional setting. Along with these methodological developments, we conduct numerical experiments with synthetic and real data to demonstrate the performance of the new methods.