Consistent and Efficient Reconstruction of Latent Tree Models
The authors study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. They propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Their first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups. Their second and main algorithm, CLGrouping, starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step guides subsequent recursive grouping (or other latent-tree learning procedures) on much smaller subsets of variables.