The Computational Power of Dynamic Bayesian Networks

TL;DR

This paper explores the computational capabilities of dynamic Bayesian networks, showing that certain variants with continuous variables can perform Turing-complete computations, unlike their discrete counterparts.

Contribution

It demonstrates that dynamic Bayesian networks with continuous variables are Turing-complete and can be simulated in real time using modified belief propagation algorithms.

Findings

Discrete dynamic Bayesian networks are no more powerful than hidden Markov models.

Continuous-variable dynamic Bayesian networks can perform Turing-complete computations.

Real-time simulation of such networks is feasible with algorithm modifications.

Abstract

This paper considers the computational power of constant size, dynamic Bayesian networks. Although discrete dynamic Bayesian networks are no more powerful than hidden Markov models, dynamic Bayesian networks with continuous random variables and discrete children of continuous parents are capable of performing Turing-complete computation. With modified versions of existing algorithms for belief propagation, such a simulation can be carried out in real time. This result suggests that dynamic Bayesian networks may be more powerful than previously considered. Relationships to causal models and recurrent neural networks are also discussed.