29,205 research outputs found
Learning Latent Tree Graphical Models
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
Markov Network Structure Learning via Ensemble-of-Forests Models
Real world systems typically feature a variety of different dependency types
and topologies that complicate model selection for probabilistic graphical
models. We introduce the ensemble-of-forests model, a generalization of the
ensemble-of-trees model. Our model enables structure learning of Markov random
fields (MRF) with multiple connected components and arbitrary potentials. We
present two approximate inference techniques for this model and demonstrate
their performance on synthetic data. Our results suggest that the
ensemble-of-forests approach can accurately recover sparse, possibly
disconnected MRF topologies, even in presence of non-Gaussian dependencies
and/or low sample size. We applied the ensemble-of-forests model to learn the
structure of perturbed signaling networks of immune cells and found that these
frequently exhibit non-Gaussian dependencies with disconnected MRF topologies.
In summary, we expect that the ensemble-of-forests model will enable MRF
structure learning in other high dimensional real world settings that are
governed by non-trivial dependencies.Comment: 13 pages, 6 figure
Learning to Discover Sparse Graphical Models
We consider structure discovery of undirected graphical models from
observational data. Inferring likely structures from few examples is a complex
task often requiring the formulation of priors and sophisticated inference
procedures. Popular methods rely on estimating a penalized maximum likelihood
of the precision matrix. However, in these approaches structure recovery is an
indirect consequence of the data-fit term, the penalty can be difficult to
adapt for domain-specific knowledge, and the inference is computationally
demanding. By contrast, it may be easier to generate training samples of data
that arise from graphs with the desired structure properties. We propose here
to leverage this latter source of information as training data to learn a
function, parametrized by a neural network that maps empirical covariance
matrices to estimated graph structures. Learning this function brings two
benefits: it implicitly models the desired structure or sparsity properties to
form suitable priors, and it can be tailored to the specific problem of edge
structure discovery, rather than maximizing data likelihood. Applying this
framework, we find our learnable graph-discovery method trained on synthetic
data generalizes well: identifying relevant edges in both synthetic and real
data, completely unknown at training time. We find that on genetics, brain
imaging, and simulation data we obtain performance generally superior to
analytical methods
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