Partial abductive inference in Bayesian networks by using probability trees

The problem of partial abductive inference in Bayesian networks is, in general, more complex to solve than other inference problems as probability/evidence propagation or total abduction. When join trees are used as the graphical structure over which propagation will be carried out, the problem can be decomposed into two stages: (1) to obtain a join tree containing only the variables included in the explanation set, and (2) to solve a total abduction problem over this new join tree. In De Campos et al. (2002a) different techniques are studied in order to approach this problem, obtaining as a result that not always the methods which obtain join trees with smaller size are also those requiring less CPU time during the propagation phase. In this work we propose to use (exact and approximate) probability trees as the basic data structure for the representation of the probability distributions used during the propagation. From our experiments, we observe how the use of exact probability trees improves the efficiency of the propagation. Besides, when using approximate probability trees the method obtains very good approximations and the required resources decrease considerably.