Learning Markov networks: maximum bounded tree-width graphs

Markov networks are a common class of graphical models used in machine learning. Such models use an undirected graph to capture dependency information among random variables in a joint probability distribution. Once one has chosen to use a Markov network model, one aims to choose the model that "best explains" the data that has been observed--this model can then be used to make predictions about future data. We show that the problem of learning a maximum likelihood Markov network given certain observed data can be reduced to the problem of identifying a maximum weight low-treewidth graph under a given input weight function. We give the first constant factor approximation algorithm for this problem. More precisely, for any fixed treewidth objective k, we find a treewidth-k graph with an f(k) fraction of the maximum possible weight of any treewidthk graph.

• Type: Conference
• Year: 2001
• Where: SODA
• Authors: David R. Karger, Nathan Srebro
• Keywords: Algorithms, Markov Network, Markov Network Model, Maximum Likelihood Markov, SODA 2001