Tree Density Estimation

We study graph estimation and density estimation in high dimensions. To avoid the curse of dimensionality, we consider a family of density estimators based on tree structured undirected graphical models. We do not assume the true distribution corresponds to a tree; rather, we try to find the best tree-based approximation to the true distribution. We apply the Chow-Liu algorithm to kernel density estimates to build a tree and then use a data-splitting scheme to choose the number of edges. We also prove oracle properties on both function estimation and structure learning.