461 research outputs found
Discovering Graphical Granger Causality Using the Truncating Lasso Penalty
Components of biological systems interact with each other in order to carry
out vital cell functions. Such information can be used to improve estimation
and inference, and to obtain better insights into the underlying cellular
mechanisms. Discovering regulatory interactions among genes is therefore an
important problem in systems biology. Whole-genome expression data over time
provides an opportunity to determine how the expression levels of genes are
affected by changes in transcription levels of other genes, and can therefore
be used to discover regulatory interactions among genes.
In this paper, we propose a novel penalization method, called truncating
lasso, for estimation of causal relationships from time-course gene expression
data. The proposed penalty can correctly determine the order of the underlying
time series, and improves the performance of the lasso-type estimators.
Moreover, the resulting estimate provides information on the time lag between
activation of transcription factors and their effects on regulated genes. We
provide an efficient algorithm for estimation of model parameters, and show
that the proposed method can consistently discover causal relationships in the
large , small setting. The performance of the proposed model is
evaluated favorably in simulated, as well as real, data examples. The proposed
truncating lasso method is implemented in the R-package grangerTlasso and is
available at http://www.stat.lsa.umich.edu/~shojaie.Comment: 12 pages, 4 figures, 1 tabl
Penalized Likelihood Methods for Estimation of Sparse High Dimensional Directed Acyclic Graphs
Directed acyclic graphs (DAGs) are commonly used to represent causal
relationships among random variables in graphical models. Applications of these
models arise in the study of physical, as well as biological systems, where
directed edges between nodes represent the influence of components of the
system on each other. The general problem of estimating DAGs from observed data
is computationally NP-hard, Moreover two directed graphs may be observationally
equivalent. When the nodes exhibit a natural ordering, the problem of
estimating directed graphs reduces to the problem of estimating the structure
of the network. In this paper, we propose a penalized likelihood approach that
directly estimates the adjacency matrix of DAGs. Both lasso and adaptive lasso
penalties are considered and an efficient algorithm is proposed for estimation
of high dimensional DAGs. We study variable selection consistency of the two
penalties when the number of variables grows to infinity with the sample size.
We show that although lasso can only consistently estimate the true network
under stringent assumptions, adaptive lasso achieves this task under mild
regularity conditions. The performance of the proposed methods is compared to
alternative methods in simulated, as well as real, data examples.Comment: 19 pages, 8 figure
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