Exploiting qualitative domain knowledge for learning Bayesian network parameters with incomplete data

When a large amount of data are missing, or when multiple hidden nodes exist, learning parameters in Bayesian networks (BNs) becomes extremely difficult. This paper presents a learning algorithm to incorporate qualitative domain knowledge to regularize the otherwise ill-posed problem, limit the search space, and avoid local optima. Specifically, the problem is formulated as a constrained optimization problem, where an objective function is defined as a combination of the likelihood function and penalty functions constructed from the qualitative domain knowledge. Then, a gradient-descent procedure is systematically integrated with the E-step and M-step of the EM algorithm, to estimate the parameters iteratively until it converges. The experiments show our algorithm improves the accuracy of the learned BN parameters significantly over the conventional EM algorithm.