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 incorpo-rate 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 combina-tion of the likelihood function and penalty functions constructed from the qualitative domain knowledge. Then, a gradient-descent procedure is systematically in-tegrated with the E-step and M-step of the EM algo-rithm, to estimate the parameters iteratively until it con-verges. The experiments show our algorithm improves the accuracy of the learned BN parameters significantly over the conventional EM algorithm.