Time Varying Dynamic Bayesian Network for Nonstationary Events Modeling and Online Inference

Abstract

This paper presents a novel time varying dynamic Bayesian network (TVDBN) model for the analysis of nonstationary sequences which are of interest in many fields. The changing network structure and parameter in TVDBN are treated as random processes whose values at each time epoch determine a stationary DBN model; this DBN model is then used to specify the distribution of data sequence at the time epoch. Under such a hierarchical formulation, the changing state of network can be incorporated into the Bayesian framework straightforwardly. The network state is assumed to transit smoothly in the joint space of numerical parameter and graphical topology so that we can achieve robust online network learning even without abundant observations. Particle filtering is employed to dynamically update current network state as well as infer hidden data values. We implement our time varying model for data sequences of multinomial and Gaussian distributions, while the general model framework can be used for any other distribution. Simulations on synthetic data and evaluations on video sequences both demonstrate that the proposed TVDBN is effective in modeling nonstationary sequences. Comprehensive comparisons have been made against existing nonstationary models, and our proposed model is shown to be the top performer.