Independence Decomposition in Dynamic Bayesian Networks

Abstract

Abstract. Dynamic Bayesian networks are a special type of Bayesian network that explicitly incorporate the dimension of time. They can be distinguished into repetitive and non-repetitive networks. Repetitiveness implies that the set of random variables of the network and their independence relations are the same at each time step. Due to their structural symmetry, repetitive networks are easier to use and are, therefore, often taken as the standard. However, repetitiveness is a very strong assumption, which normally does not hold, as particular dependences and independences may only hold at certain time steps. In this paper, we propose a new framework for independence modularisation in dynamic Bayesian networks. Our theory provides a method for separating atemporal and temporal independence relations, and offers a practical approach to building dynamic Bayesian networks that are possibly non-repetitive. A composition operator for temporal and atemporal independence relations is proposed and its properties are studied. Experimental results obtained by learning dynamic Bayesian networks from real data show that this framework offers a more accurate way for knowledge representation in dynamic Bayesian networks.

Learning Bayesian networks: approaches and issues

“…Boyen et al (1999) looked at a way of using SEM in learning DBNs and in particular found a novel approach to detecting hidden variables in dynamic systems. And while DBNs are generally constant over time, it is possible to learn DBNs that change as time progresses (Flesch & Lucas, 2007;Robinson & Hartemink, 2009) and indeed learn DBNs from non-temporal data (La¨hdesma¨ki & Shmulevich, 2008). Murphy and Mian (1999) show how DBNs subsume many other dynamic models into a general framework and look at the various tasks that need to be done to learn a DBN.…”

“…More information of DBNs can be found in the papers of Dean and Kanazawa (1989) and Friedman et al (1998) and in the work of Murphy and Mian (1999). In addition, Ghahramani (1998) examines the topic from the perspective of learning and Flesch and Lucas (2007) consider DBNs where the transition network can change over time. Learning Bayesian networks: approaches and issues…”

“…Murphy and Mian (1999) show how DBNs subsume many other dynamic models into a general framework and look at the various tasks that need to be done to learn a DBN. And while DBNs are generally constant over time, it is possible to learn DBNs that change as time progresses (Flesch & Lucas, 2007;Robinson & Hartemink, 2009) and indeed learn DBNs from non-temporal data (La¨hdesma¨ki & Shmulevich, 2008).…”

“…examines the topic from the perspective of learning andFlesch and Lucas (2007) consider DBNs where the transition network can change over time. Bayesian networks do not specify what to do in a particular situation; they only say…”

Computational algorithm for dynamic hybrid Bayesian network in on-line system health management applications

“…In addition Murphy and Mian (Murphy & Mian, 1999) show modeling of data using DBN. Ghahramani (Ghahramani, 1998) examines the topic from the perspective of learning and Flesch and Lucas (Flesch & Lucas, 2007) consider DBNs where the transition network can change over time.…”