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Learning Model Parameters When Data Are Incomplete


 Given a graphical model, a serious issue is how to automatically learn the model parameters from available training data. When a significant amount of data are missing, or when multiple hidden nodes exist, which is common for many real-world applications, learning parameters in probabilistic graphical models becomes extremely difficult, due to the large search space and the presence of many local maxima. Various learning algorithms are proposed to address this challenge. However, most of them fail to exploit the available domain knowledge, which is critical to regularize this otherwise ill-posed problem. This motivates us to propose a learning algorithm that overcomes the limitations of the existing methods by systematically incorporating the prior knowledge into the learning process. Instead of using the likelihood function as the objective to maximize during learning, we define the objective function as a combination of the likelihood function and the penalty functions constructed from the 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 learning algorithms have been applied to several applications including facial action unit recognition, human affective state recogntioin, and battlefield stituation assessment. The experiments showed our algorithm can improve the accuracy of the learned BN parameters significantly over the conventional EM algorithm.








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