Integrating approximate single factor graphical models

In the analysis of complex and high-dimensional data, graphical models have been commonly adopted to describe associations among variables. When common factors exist which make the associations dense, the single factor graphical model has been proposed, which first extracts the common factor and then conducts graphical modeling. Under other simpler contexts, it has been recognized that results generated from analyzing a single dataset are often unsatisfactory, and integrating multiple datasets can effectively improve variable selection and estimation. In graphical modeling, the increased number of parameters makes the "lack of information" problem more severe. In this article, we integrate multiple datasets and conduct the approximate single factor graphical model analysis. A novel penalization approach is developed for the identification and estimation of important loadings and edges. An effective computational algorithm is developed. A wide spectrum of simulations and the analysis of breast cancer gene expression datasets demonstrate the competitive performance of the proposed approach. Overall, this study provides an effective new venue for taking advantage of multiple datasets and improving graphical model analysis.