Learning Bayesian network parameters from small data set: A spatially maximum a posteriori method

To learn accurate BN parameters from small data set, combined with data, domain knowledge is often incorporated into the learning process as parameter constraints. Currently, most of the existing parameter learning methods take parameter learning problem as an exact optimization problem and regard the optimal solutions as the final parameters. However, due to the scarcity of data, objective functions constructed from the data, like likelihood function and entropy function, are not accurate. Therefore, parameters derived from the objective functions do not approach the true parameters well while some suboptimal parameters fit the true parameters better. Thus, searching more reasonable suboptimal parameters is a possible approach to learn better BN parameters. In this paper, we propose to visualize suboptimal parameters with parallel coordinate system and propose a Spatially Maximum a Posteriori (SMAP) method. Experimental results reveal that the proposed method outperforms most of the existing parameter learning methods.