Estimating Dependency Structure as a Hidden Variable

This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EMand the Minimum Spanning Tree algorithm to find the ML and MAP mixtureof trees for a variety of priors, including the Dirichlet and the MDL priors.

Estimating Dependency Structure as a Hidden Variable

This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors. We also show that the single tree classifier acts like an implicit feature selector, thus making the classification performance insensitive to irrelevant attributes. Experimental results demonstrate the excellent performance of the new model both in density estimation and in classification.

An Accelerated Chow and Liu Algorithm: Fitting Tree Distributions to High Dimensional Sparse Data

Chow and Liu introduced an algorithm for fitting a multivariate distribution with a tree (i.e. a density model that assumes that there are only pairwise dependencies between variables) and that the graph of these dependencies is a spanning tree. The original algorithm is quadratic in the dimesion of the domain, and linear in the number of data points that define the target distribution $P$. This paper shows that for sparse, discrete data, fitting a tree distribution can be done in time and memory that is jointly subquadratic in the number of variables and the size of the data set. The new algorithm, called the acCL algorithm, takes advantage of the sparsity of the data to accelerate the computation of pairwise marginals and the sorting of the resulting mutual informations, achieving speed ups of up to 2-3 orders of magnitude in the experiments.