Model Complexity of Pseudo-independent Models

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A type of problem domains known as pseudo-independent (PI) domains poses difficulty for common probabilistic learning methods based on the single-link lookahead search. To learn this type of domain models, a learning method based on the multiple-link lookahead search is needed. An improved result can be obtained by incorporating model complexity into a scoring metric to explicitly trade off model accuracy for complexity and vice versa during selection of the best model among candidates at each learning step. To implement this scoring metric for the PI-learning method, the complexity formula for PI models is required. Previous studies found the complexity formula for full PI models, one of the three major types of PI models (the other two are partial and mixed PI models). This study presents the complexity formula for atomic partial PI models, partial PI models that contain no embedded PI submodels. The complexity is acquired by arithmetic operation on the spaces of domain variables. The new formula provides the basis for further characterizing the complexity of non-atomic PI models, which contain embedded PI submodels in their domains.