Learning Latent Tree Graphical Models

by   Myung Jin Choi, et al.

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.


page 1

page 2

page 3

page 4


Latent tree models

Latent tree models are graphical models defined on trees, in which only ...

Spectral Methods for Learning Multivariate Latent Tree Structure

This work considers the problem of learning the structure of multivariat...

Robustifying Algorithms of Learning Latent Trees with Vector Variables

We consider learning the structures of Gaussian latent tree models with ...

Spectral Top-Down Recovery of Latent Tree Models

Modeling the distribution of high dimensional data by a latent tree grap...

Learning Vector Autoregressive Models with Latent Processes

We study the problem of learning the support of transition matrix betwee...

Inference in balanced community modulated recursive trees

We introduce a random recursive tree model with two communities, called ...

Unfolding Latent Tree Structures using 4th Order Tensors

Discovering the latent structure from many observed variables is an impo...

Please sign up or login with your details

Forgot password? Click here to reset