On Directed and Undirected Propagation Algorithms for Bayesian Networks

Message-passing inference algorithms for Bayes nets can be broadly divided into two classes: i) clustering algorithms, like Lazy Propagation, Jensen’s or Shafer-Shenoy’s schemes, that work on secondary undirected trees; and ii) conditioning methods, like Pearl’s, that use directly Bayes nets. It is commonly thought that algorithms of the former class always outperform those of the latter because Pearl’s-like methods act as particular cases of clustering algorithms. In this paper, a new variant of Pearl’s method based on a secondary directed graph is introduced, and it is shown that the computations performed by Shafer-Shenoy or Lazy propagation can be precisely reproduced by this new variant, thus proving that directed algorithms can be as efficient as undirected ones.