Learning Latent Tree Graphical Models

Myung Jin Choi, Vincent Y. F. Tan, Animashree Anandkumar, Alan S. Willsky

Massachusetts Institute of Technology


We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes.

Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions.

We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset.


"Learning Latent Tree Graphical Models"
Myung Jin Choi, Vincent Y. F. Tan, Animashree Anandkumar, and Alan S. Willsky
To appear in the Journal of Machine Learning Research, 2011

"Consistent and Efficient Reconstruction of Latent Tree Models"
Myung Jin Choi, Vincent Y. F. Tan, Animashree Anandkumar, and Alan S. Willsky
Allerton Conference, 2010.


Download the MATLAB implementation : latentTree.tar

- compute_recovery_rate.m compares the performance of different algorithms on synthetic datasets.

- learn_sp100_tree.m learns a latent tree to model the dependency structure of monthly stock returns (Gaussian variables).

- learn_discrete_latent_tree.m learns a latent tree for the 20 Newsgroups dataset with 100 words (binary variables). A part of the code that computes the log-likelihood of the learned tree for performance evaluation is modified from the code by Stefan Harmeling.


This work was supported in part by AFOSR under Grant FA9550-08-1-1080 and in part by MURI under AFOSR Grant FA9550-06-1-0324. Vincent Tan is also supported by A*STAR, Singapore.