A network model that combines latent factors and sparse graphs. (23rd December 2020)

• Record Type: Journal Article
• Authors: Suh, Namjoon; Huo, Xiaoming; Heim, Eric; Seversky, Lee
• Is Part Of: Statistical analysis and data mining. Volume 14:Number 2(2021)
• Page Start: 97
• Page End: 115
• Publication Date: 2020-12-23
• Subjects: alternating direction method of multiplier -- convex optimization -- latent variable model -- logistic regression model -- low rank matrix -- matrix decomposition -- sparse matrix; Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11492
• Languages: English
• ISSNs: 1932-1864

Abstract

Abstract: We propose a combined model, which integrates the latent factor model and a sparse graphical model, for network data. It is noticed that neither a latent factor model nor a sparse graphical model alone may be sufficient to capture the structure of the data. The proposed model has a latent (i.e., factor analysis) model to represent the main trends (a.k.a., factors), and a sparse graphical component that captures the remaining ad‐hoc dependence. Model selection and parameter estimation are carried out simultaneously via a penalized likelihood approach. The convexity of the objective function allows us to develop an efficient algorithm, while the penalty terms push towards low‐dimensional latent components and a sparse graphical structure. The effectiveness of our model is demonstrated via simulation studies, and the model is also applied to four real datasets: Zachary's Karate club data, Kreb's U.S. political book dataset ( http://www.orgnet.com ), U.S. political blog dataset, and citation network of statisticians; showing meaningful performances in practical situations.