Learning Latent Tree Graphical Models
Abstract
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 algorithms can be applied to both discrete and Gaussian random variables and our learned models are such that all the observed and latent variables have the same domain (state space). 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 such as neighbor-joining) 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 data sets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups data set.
Additional Information
© 2011 Myung Jin Choi, Vincent Y. F. Tan, Animashree Anandkumar and Alan S. Willsky. Submitted 9/10; Revised 2/11; Published 5/11. This research was supported in part by Shell International Exploration and Production, Inc. and in part by the Air Force Office of Scientific Research under Award No. FA9550-06-1-0324. This work was also supported in part by AFOSR under Grant FA9550-08-1-1080 and in part by MURI under AFOSR Grant FA9550-06-1-0324. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Air Force. Vincent Tan and Animashree Anandkumar are supported by A*STAR, Singapore and by the setup funds at U.C. Irvine respectively.Attached Files
Published - choi11b.pdf
Submitted - 1009.2722.pdf
Files
Name | Size | Download all |
---|---|---|
md5:cfb200e24d040f0836c624015e9ddf62
|
734.6 kB | Preview Download |
md5:fdd549d2c1a4bd1c1b9e2aab3041f36b
|
881.1 kB | Preview Download |
Additional details
- Eprint ID
- 81875
- Resolver ID
- CaltechAUTHORS:20170927-100701408
- Shell International Exploration and Production, Inc.
- Air Force Office of Scientific Research (AFOSR)
- FA9550-06-1-0324
- Air Force Office of Scientific Research (AFOSR)
- FA9550-08-1-1080
- Air Force Office of Scientific Research (AFOSR)
- FA9550-06-1-0324
- Agency for Science, Technology and Research (A*STAR)
- University of California, Irvine
- Created
-
2017-09-27Created from EPrint's datestamp field
- Updated
-
2023-06-02Created from EPrint's last_modified field