Joint Estimation of Multiple Graphical Models From Heterogeneous Subpopulations
Open Access
- Author:
- Moysidis, Ilias
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- April 02, 2021
- Committee Members:
- Bing Li, Dissertation Advisor/Co-Advisor
Bing Li, Committee Chair/Co-Chair
Bharath Kumar Sriperumbudur, Committee Member
Runze Li, Committee Member
Alexei Novikov, Outside Member
Ephraim Mont Hanks, Program Head/Chair - Keywords:
- Graphical Models
Joint estimation
heterogeneous subpopulations
neighborhood selection
variable selection
nonsmooth optimization
functional graphical models - Abstract:
- It is a frequent occurrence in the field of graphical models to estimate graphs from different subpopulations that share behavioral or genetic similarities. For example, such subpopulations can be alcoholic and non-alcoholic groups, cancer and non-cancer patients, students and faculty. We can expect these similarities to translate into a common graph structure. Compiling all the data together to estimate a single graph would ignore the differences among subpopulations. Dividing the data to estimate a graph for each subpopulation separately does not make efficient use of the common structure in the data. It is therefore crucial to develop methods for combining all the data to estimate the graphs of the subpopulations simultaneously. My research with Dr.Bing Li is focused on two important areas of simultaneous graph estimation: \textbf{(1)} the simultaneous estimation of functional graphical models by graphical lasso, \textbf{(2)} the simultaneous estimation of high-dimensional graphical models by neighborhood selection. Concerning \textbf{(1)}, functional graphical models explore dependence relationships of random processes. This is achieved through estimating the precision matrix of the coefficients from the Karhunen-Loeve expansion. Our research deals with the problem of estimating functional graphs that consist of the same random processes and share some of the dependence structure. Concerning \textbf{(2)}, we develop a new method for simultaneous estimation of multiple graphical models by estimating the topological neighborhoods of the involved variables under a sparse inducing penalty that takes into account the common structure in the subpopulations. Unlike the existing methods for joint graphical models, our method does not rely on spectral decomposition of large matrices, and is therefore more computationally attractive for estimating large networks.