Exact Learning of Bounded Tree-width Bayesian Networks
نویسندگان
چکیده
Inference in Bayesian networks is known to be NP-hard, but if the network has bounded treewidth, then inference becomes tractable. Not surprisingly, learning networks that closely match the given data and have a bounded tree-width has recently attracted some attention. In this paper we aim to lay groundwork for future research on the topic by studying the exact complexity of this problem. We give the first non-trivial exact algorithm for the NP-hard problem of finding an optimal Bayesian network of tree-width at most w, with running time 3nnw+O(1), and provide an implementation of this algorithm. Additionally, we propose a variant of Bayesian network learning with “super-structures”, and show that finding a Bayesian network consistent with a given super-structure is fixedparameter tractable in the tree-width of the super-structure.
منابع مشابه
Learning Bounded Tree-Width Bayesian Networks via Sampling
Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [12, 14] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. In this paper, we propose a sampling method to efficiently find representative k-trees by introducing ...
متن کاملLearning Bayesian Networks with Bounded Tree-width via Guided Search
Bounding the tree-width of a Bayesian network can reduce the chance of overfitting, and allows exact inference to be performed efficiently. Several existing algorithms tackle the problem of learning bounded tree-width Bayesian networks by learning from k-trees as super-structures, but they do not scale to large domains and/or large tree-width. We propose a guided search algorithm to find k-tree...
متن کاملEfficient learning of Bayesian networks with bounded tree-width
Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [24, 29] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. Finding the best k-tree, however, is computationally intractable. In this paper, we propose a sampling...
متن کاملTractable Bayesian Network Structure Learning with Bounded Vertex Cover Number
Both learning and inference tasks on Bayesian networks are NP-hard in general. Bounded tree-width Bayesian networks have recently received a lot of attention as a way to circumvent this complexity issue; however, while inference on bounded tree-width networks is tractable, the learning problem remains NP-hard even for tree-width 2. In this paper, we propose bounded vertex cover number Bayesian ...
متن کاملLearning Bounded Tree-width Bayesian Networks using Integer Linear Programming
In many applications one wants to compute conditional probabilities given a Bayesian network. This inference problem is NP-hard in general but becomes tractable when the network has low tree-width. Since the inference problem is common in many application areas, we provide a practical algorithm for learning bounded tree-width Bayesian networks. We cast this problem as an integer linear program ...
متن کامل