Learning Bayesian network classifiers with completed partially directed acyclic graphs
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Proceedings of the Ninth International Conference on Probabilistic Graphical Models, PMLR 72:272283, 2018.
Abstract
Most search and score algorithms for learning Bayesian network classifiers from data traverse the space of directed acyclic graphs (DAGs), making arbitrary yet possibly suboptimal arc directionality decisions. This can be remedied by learning in the space of DAG equivalence classes. We provide a number of contributions to existing work along this line. First, we identify the smallest subspace of DAGs that covers all possible classposterior distributions when data is complete. All the DAGs in this space, which we call \textit{minimal classfocused} DAGs (MCDAGs), are such that their every arc is directed towards a child of the class variable. Second, in order to traverse the equivalence classes of MCDAGs, we adapt the greedy equivalence search (GES) by adding operator validity criteria which ensure GES only visits states within our space. Third, we specify how to efficiently evaluate the discriminative score of a GES operator for MCDAG in time independent of the number of variables and without converting the completed partially DAG, which represents an equivalence class, into a DAG. The adapted GES perfomed well on realworld data sets.
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