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2015 ; 2015
(ä): 2617-2623
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Pathway Graphical Lasso
#MMPMID26167394
Grechkin M
; Fazel M
; Witten D
; Lee SI
Proc AAAI Conf Artif Intell
2015[Jan]; 2015
(ä): 2617-2623
PMID26167394
show ga
Graphical models provide a rich framework for summarizing the dependencies among
variables. The graphical lasso approach attempts to learn the structure of a
Gaussian graphical model (GGM) by maximizing the log likelihood of the data,
subject to an l(1) penalty on the elements of the inverse co-variance matrix.
Most algorithms for solving the graphical lasso problem do not scale to a very
large number of variables. Furthermore, the learned network structure is hard to
interpret. To overcome these challenges, we propose a novel GGM structure
learning method that exploits the fact that for many real-world problems we have
prior knowledge that certain edges are unlikely to be present. For example, in
gene regulatory networks, a pair of genes that does not participate together in
any of the cellular processes, typically referred to as pathways, is less likely
to be connected. In computer vision applications in which each variable
corresponds to a pixel, each variable is likely to be connected to the nearby
variables. In this paper, we propose the pathway graphical lasso, which learns
the structure of a GGM subject to pathway-based constraints. In order to solve
this problem, we decompose the network into smaller parts, and use a
message-passing algorithm in order to communicate among the subnetworks. Our
algorithm has orders of magnitude improvement in run time compared to the
state-of-the-art optimization methods for the graphical lasso problem that were
modified to handle pathway-based constraints.