Marginal information for structure learning

Abstract

This thesis is devoted to introduce methods for incorporating the marginal information in structure learning of graphical models. As the number of variables involved in the model increases, the performance of structure learning decreases due to the size of the large search space and the limited sample size. On the other hand, marginal models can be obtained more easily from the domain experts or the same data set because they include only some subsets of variables. This thesis propose two methods to improve the performance of the whole structure learning by using these marginal model structuresIn the first part, we improve the score-based learning of Bayesian networks by using marginal models. structure learning for Bayesian networks has been made in a heuristic mode in search of an optimal model to avoid an explosive computational burden. In the learning process, a structural error which occurred at a point of learning may deteriorate its subsequent learning. We proposed a remedial approach to this error-for-error process by using marginal model structures. The remedy is made by xing local errors in structure in reference to the marginal structures. In this sense, we call the remedy a marginally corrective procedure. We devised a new score function for the procedure which consists of two components, the likelihood function of a model and a discrepancy measure in marginal structures. The proposed method compares favorably with a couple of the most popular algorithms as shown in experiments with benchmark data sets.In the second part of the thesis, we propose a structure learning method by combining marginal model structures. In many domains, data can be obtained from various sources and each may not contains all the variables involved in the system depending on the environment in which the data is collected. The graph constructed for each dataset can be considered as a marginal model of the entire model and they need to be combined for a joint inference. We propose methods of nding the complete set of possible combined model structures for undirected graphs. The proposed method outperforms the existing method as shown in our experiment.