Efficient Inference in Large Graphical Models Using Bayesian Non-Negative Tensor Decompositions

• Activity Number: 187
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Hongxia Yang*+ and Yinglong Xia and Yasuo Amemiya and Ching-Yung Lin
• Companies: IBM T.J. Watson Research Center and IBM T.J. Watson Research Center and IBM T.J. Watson Research Center and IBM T.J. Watson Research Center
• Keywords: graphical model ; Bayesian statistics ; nonnegative Tensor decompositions

Abstract

Graphical models are commonly used probability distribution models in which the structure of interactions among random variables is captured by a graph. As a powerful tool to describe complex high-dimensional systems specified through local interactions, graphical models are extremely rich and expressive for a diverse range of phenomena. Despite of the popularity of graphical models, inference has been known as a fundamental challenge in large scale graphical models. To address this problem, we propose a series of increasingly sophisticated graphical models, based on Bayesian nonnegative Tensor Factorization. In this way, standard operations in inference such as the absorption, marginalization, and extension can be efficiently implemented using the approximate potential tables transformed by tensor factorization. As a result, our proposed technique not only accelerates inference computation but also avoids dramatic increase of potential table sizes in large scale graphical models. We evaluated the proposed models using both simulated datasets as well as practical applications. The experiments demonstrate that the proposed models outperform the state-of-the-art approaches.