Exploiting Functional Dependence in Bayesian Network Inference

In this paper we propose an efficient method for Bayesian network inference in models with functional dependence. We generalize the multiplicative factorization method originally designed by Takikawa and D'Ambrosio (1999) for models with independence of causal influence. Using a hidden variable, we transform a probability potential into a product of two-dimensional potentials. The multiplicative factorization yields more efficient inference. For example, in junction tree propagation it helps to avoid large cliques. In order to keep potentials small, the number of states of the hidden variable should be minimized. We transform this problem into a combinatorial problem of minimal base in a particular space. We present an example of a computerized adaptive test, in which the factorization method is significantly more efficient than previous inference methods.