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 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.