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Entropy 2018, 20(4), 274; https://doi.org/10.3390/e20040274

Polynomial-Time Algorithm for Learning Optimal BFS-Consistent Dynamic Bayesian Networks

Instituto de Telecomunicações, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
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Received: 22 March 2018 / Revised: 5 April 2018 / Accepted: 10 April 2018 / Published: 12 April 2018
(This article belongs to the Special Issue Information Theory in Machine Learning and Data Science)
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Abstract

Dynamic Bayesian networks (DBN) are powerful probabilistic representations that model stochastic processes. They consist of a prior network, representing the distribution over the initial variables, and a set of transition networks, representing the transition distribution between variables over time. It was shown that learning complex transition networks, considering both intra- and inter-slice connections, is NP-hard. Therefore, the community has searched for the largest subclass of DBNs for which there is an efficient learning algorithm. We introduce a new polynomial-time algorithm for learning optimal DBNs consistent with a breadth-first search (BFS) order, named bcDBN. The proposed algorithm considers the set of networks such that each transition network has a bounded in-degree, allowing for p edges from past time slices (inter-slice connections) and k edges from the current time slice (intra-slice connections) consistent with the BFS order induced by the optimal tree-augmented network (tDBN). This approach increases exponentially, in the number of variables, the search space of the state-of-the-art tDBN algorithm. Concerning worst-case time complexity, given a Markov lag m, a set of n random variables ranging over r values, and a set of observations of N individuals over T time steps, the bcDBN algorithm is linear in N, T and m; polynomial in n and r; and exponential in p and k. We assess the bcDBN algorithm on simulated data against tDBN, revealing that it performs well throughout different experiments. View Full-Text
Keywords: dynamic Bayesian networks; optimum branching; score-based learning; theoretical-information scores dynamic Bayesian networks; optimum branching; score-based learning; theoretical-information scores
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Sousa, M.; Carvalho, A.M. Polynomial-Time Algorithm for Learning Optimal BFS-Consistent Dynamic Bayesian Networks. Entropy 2018, 20, 274.

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