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Learning Latent Tree Graphical Models
Machine Learning · Submitted 14 Sep 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This results in more accurate and efficient learning of latent trees.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. | background 0.95 | 0.25 | 0.04 | asserted 0.87 |
| s1 | We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. | contribution 0.99 | 0.95 | 0.22 | asserted 1.00 |
| s2 | Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. | contribution 0.92 | 0.31 | 0.05 | asserted 1.00 |
| s3 | Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. | method 0.98 | 0.90 | 0.05 | asserted 1.00 |
| s4 | One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. | contribution 1.00 | 0.92 | 0.10 | asserted 0.99 |
| s5 | CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. | method 0.98 | 0.85 | 0.04 | asserted 1.00 |
| s6 | 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. | method 0.99 | 0.81 | 0.16 | asserted 0.80 |
| s7 | This results in more accurate and efficient learning of latent trees. | result 0.60 | 0.69 | 0.29 | asserted 1.00 |
| s8 | We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. | contribution 0.90 | 0.93 | 0.07 | asserted 1.00 |
| s9 | 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. | method 0.72 | 0.96 | 0.07 | asserted 0.98 |
| s10 | 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. | contribution 0.69 | 0.96 | 0.09 | asserted 1.00 |
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The paper
Original 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 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.
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References
How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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In parametric settings, [ref] and [ref] develop algorithms and theory for learning graphical models with latent variables.
Sparse Nonparametric Graphical Models · Discussion · 0.90
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Choi et al. developed methods based on Chow and Liu's to learn dependence tree approximations of distributions with hidden variables [ref] .
Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes · Related work · 0.85
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