Learning Sparse Markov Network Structure via Ensemble-of-Trees Models

Learning the sparse structure of a general Markov network is a hard computational problem. One of the main difficulties is the computation of the generally intractable partition function. To circumvent this difficulty, we propose to learn the network structure using an ensemble-oftrees (ET) model. The ET model was first introduced by Meilă and Jaakkola (2006), and it represents a multivariate distribution using a mixture of all possible spanning trees. The advantage of the ET model is that, although it needs to sum over super-exponentially many trees, its partition function as well as data likelihood can be computed in a closed form. Furthermore, because the ET model tends to represent a Markov network using as small number of trees as possible, it provides a natural regularization for finding a sparse network structure. Our simulation results show that the proposed ET approach is able to accurately recover the true Markov network connectivity and outperform the state-of-art approaches for both discrete and continuous random variable networks when a small number of data samples is available. Furthermore, we also demonstrate the usage of the ET model for discovering the network of words from blog posts.