Exact Distributed Structure-Learning for Bayesian Networks
Keywords: Bayesian networks, Causality, Structure learning, Distributed learning
Abstract: Learning the structure of a Bayesian network is currently practical for only a limited number of variables. Existing distributed learning approaches approximate the true structure. We present an exact distributed structure-learning algorithm to find a P-map for a set of random variables. First, by using conditional independence, the variables are divided into sets $\X_1,\ldots,\X_I$ such that for each $\X_i$, the presence and absence of edges that are adjacent with any interior node (a node that is not in any other $\X_j, j\neq i$) can be correctly identified by learning the structure of $\X_i$ separately without using the information of the variables other than $\X_i$. Second, constraint or score-based structure learners are employed to learn the P-map of $\X_i$, in a decentralized way. Finally, the separately learned structures are appended by checking a conditional independence test on the boundary nodes (those that are in at least two $\X_i$'s). The result is proven to be a P-map. This approach allows for a significant reduction in computation time and opens the door for structure learning for a ``giant'' number of variables.
Primary Area: learning theory
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Submission Number: 12513
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