Sparse Multidimensional Graphical Models: A Unified Framework

• Activity Number: 313
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yang Ni* and Francesco Stingo and Veera Baladandayuthapani
• Companies: Rice University and MD Anderson Cancer Center and MD Anderson Cancer Center
• Keywords: Directed acyclic graphs ; Decomposable and non-decomposable ; Partially collapsed Gibbs sampler ; LDL decomposition ; Poisson log-linear model

Abstract

Multi-dimensional data with measurement along multiple axes have emerged in many scientific areas such as genomics and cancer surveillance. Traditional multivariate analysis approaches are unsuitable for such highly structured data due to inefficiency, loss of power and lack of interpretability. In this paper, we propose a novel multi-dimensional graphical model based on matrix decomposition of precision matrix for multi-dimensional data. Our approach is a unified framework as it can be used to model both directed and undirected graphs. We fully exploit the marginalization of the likelihood and employ partially collapsed Gibbs sampler for efficient sampling. Empirically, through simulation studies, we show the superior performance of our approach in comparison with benchmark and state-of-the-art methods. Finally, we apply our approach to two datasets: ovarian cancer proteomics and U.S. cancer mortality.