Gaussian Message Propagation in d-order Neighborhood for Gaussian Graphical Model

Abstract

AbstractGaussian graphical models are important undirected graphical models with multivariate Gaussian distribution. A key probabilistic inference problem for the model is to compute the marginals. Exact inference algorithms have cubic computational complexity, which is intolerable for large-scale models. Most of approximate inference algorithms have a form of message iterations, and their computational complexity is closely related to the convergence and convergence rate, which causes the uncertain computational efficiency. In this paper, we design a fixed parameter linear time approximate algorithm — the Gaussian message propagation in d-order neighborhood. First, we define the d-order neighborhood concept to describe the propagation scope of exact Gaussian messages. Then we design the algorithm of Gaussian message propagation in d-order neighborhood, which propagates Gaussian messages in variable’s d-order neighborhood exactly, and in the (d + 1)th-order neighborhood partly to preserve the spread of the Gaussian messages, and computes the approximate marginals in linear time O(n·d 2) with the fixed parameter d. Finally, we present verification experiments and comparison experiments, and analyze the experiment results.KeywordsGaussian graphical modelProbabilistic inferenceMessage propagation d-order neighborhood