Goal Oriented Symbolic Propagation in Bayesian Networks

The paper presents an efficient goal oriented algorithm for symbolic propagation in Bayesian networks. The proposed algorithm performs symbolic propagation using numerical methods. It first takes advantage of the independence relationships among the variables and produce a reduced graph which contains only the relevant nodes and parameters required to compute the desired propagation. Then, the symbolic expression of the solution is obtained by performing numerical propagations associated with specific values of the symbolic parameters. These specific values are called the canonical components. Substantial savings are obtained with this new algorithm. Furthermore, the canonical components allow us to obtain lower and upper bounds for the symbolic expressions resulting from the propagation. An example is used to illustrate the proposed methodology.