The Computational Power of Dynamic Bayesian Networks
This foundational insight into the computational limits of probabilistic models could impact fields like AI and machine learning by revealing new capabilities for complex reasoning.
The paper demonstrates that dynamic Bayesian networks with continuous random variables and discrete children of continuous parents can perform Turing-complete computation, suggesting greater computational power than previously thought, with real-time simulation enabled by modified belief propagation algorithms.
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.