116 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
Generalized Score Matching for Non-Negative Data
A common challenge in estimating parameters of probability density functions
is the intractability of the normalizing constant. While in such cases maximum
likelihood estimation may be implemented using numerical integration, the
approach becomes computationally intensive. The score matching method of
Hyv\"arinen [2005] avoids direct calculation of the normalizing constant and
yields closed-form estimates for exponential families of continuous
distributions over . Hyv\"arinen [2007] extended the approach to
distributions supported on the non-negative orthant, . In this
paper, we give a generalized form of score matching for non-negative data that
improves estimation efficiency. As an example, we consider a general class of
pairwise interaction models. Addressing an overlooked inexistence problem, we
generalize the regularized score matching method of Lin et al. [2016] and
improve its theoretical guarantees for non-negative Gaussian graphical models.Comment: 70 pages, 76 figure
- …