USING HIDDEN NODES IN BAYESIAN NETWORKS

In the construction of a Bayesian network, it is always assumed that t he variables starting from the same parent are conditionally independe nt. In practice, this assumption may not hold, and will give rise to i ncorrect inferences. In cases where some dependency is found between v ariables, we propose that the creation of a hidden node, which in effe ct models the dependency, can solve the problem. In order to determine the conditional probability matrices for the hidden node, we use a gr adient descent method. The objective function to be minimised is the s quared-error between the measured and computed values of the instantia ted nodes. Both forward and backward propagation are used to compute t he node probabilities. The error gradients can be treated as updating messages and can be propagated in any direction throughout any singly connected network. We used the simplest node-by-node creation approach for parents with more than two children. We tested our approach on tw o different networks in an endoscope guidance system and, in both case s, demonstrated improved results.