Lazy Probability Propagation on Gaussian Bayesian Networks

Novel lazy Lauritzen-Spiegelhalter (LS), lazy Hugin and lazy Shafer-Shenoy (SS) algorithms are devised for Gaussian Bayesian networks (BNs). In the lazy algorithms, the clique potentials and separator potentials are kept in combinable decomposed form instead of combined to be a single valuation in conventional junction tree algorithms. By employing decomposed form potentials, the independence relations between variables are explored online and the directed graph information is utilized in the message calculations. In the proposed algorithms, a consistent junction tree with the evidence entered can be obtained by a single round of message passing. The moments form parametrization of Gaussian distributions allows the deterministic relationships between variables. Preliminary analysis shows that the lazy LS algorithm and the lazy Hugin algorithm are more computationally efficient than the lazy SS algorithm, especially when there are multiple items of evidence to be incorporated.