Methods and Experiments With Bounded Tree-width Markov Networks
ثبت نشده
چکیده
Markov trees generalize naturally to bounded tree-width Markov networks, on which exact computations can still be done efficiently. However, learning the maximum likelihood Markov network with tree-width greater than 1 is NP-hard, so we discuss a few algorithms for approximating the optimal Markov network. We present a set of methods for training a density estimator. Each method is specified by three arguments: tree-width, model scoring metric (maximum likelihood or minimum description length), and model representation (using one joint distribution or several class-conditional distributions). On these methods, we give empirical results on density estimation and classification tasks and explore the implications of these arguments.
منابع مشابه
Methods and Experiments With Bounded Tree-width Markov Networks
Markov trees generalize naturally to bounded tree-width Markov networks, on which exact computations can still be done efficiently. However, learning the maximum likelihood Markov network with tree-width greater than 1 is NP-hard, so we discuss a few algorithms for approximating the optimal Markov network. We present a set of methods for training a density estimator. Each method is specified by...
متن کاملMaximum Likelihood Bounded Tree-Width Markov Networks
We study the problem of projecting a distribution onto (or finding a maximum likelihood distribution among) Markov networks of bounded tree-width. By casting it as the combinatorial optimization problem of finding a maximum weight hypertree, we prove that it is NP-hard to solve exactly and provide an approximation algorithm with a provable performance guarantee.
متن کاملLearning 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 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 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 کامل