94 research outputs found
iPACOSE: an iterative algorithm for the estimation of gene regulation networks
In the context of Gaussian Graphical Models (GGMs) with high-
dimensional small sample data, we present a simple procedure to esti-
mate partial correlations under the constraint that some of them are
strictly zero. This method can also be extended to covariance selection.
If the goal is to estimate a GGM, our new procedure can be applied
to re-estimate the partial correlations after a first graph has been esti-
mated in the hope to improve the estimation of non-zero coefficients. In
a simulation study, we compare our new covariance selection procedure
to existing methods and show that the re-estimated partial correlation
coefficients may be closer to the real values in important cases
Iterative reconstruction of high-dimensional Gaussian Graphical Models based on a new method to estimate partial correlations under constraints.
In the context of Gaussian Graphical Models (GGMs) with high-dimensional small sample data, we present a simple procedure, called PACOSE - standing for PArtial COrrelation SElection - to estimate partial correlations under the constraint that some of them are strictly zero. This method can also be extended to covariance selection. If the goal is to estimate a GGM, our new procedure can be applied to re-estimate the partial correlations after a first graph has been estimated in the hope to improve the estimation of non-zero coefficients. This iterated version of PACOSE is called iPACOSE. In a simulation study, we compare PACOSE to existing methods and show that the re-estimated partial correlation coefficients may be closer to the real values in important cases. Plus, we show on simulated and real data that iPACOSE shows very interesting properties with regards to sensitivity, positive predictive value and stability
Sparse Inverse Covariance Selection via Alternating Linearization Methods
Gaussian graphical models are of great interest in statistical learning.
Because the conditional independencies between different nodes correspond to
zero entries in the inverse covariance matrix of the Gaussian distribution, one
can learn the structure of the graph by estimating a sparse inverse covariance
matrix from sample data, by solving a convex maximum likelihood problem with an
-regularization term. In this paper, we propose a first-order method
based on an alternating linearization technique that exploits the problem's
special structure; in particular, the subproblems solved in each iteration have
closed-form solutions. Moreover, our algorithm obtains an -optimal
solution in iterations. Numerical experiments on both synthetic
and real data from gene association networks show that a practical version of
this algorithm outperforms other competitive algorithms
Adaptive First-Order Methods for General Sparse Inverse Covariance Selection
In this paper, we consider estimating sparse inverse covariance of a Gaussian
graphical model whose conditional independence is assumed to be partially
known. Similarly as in [5], we formulate it as an -norm penalized maximum
likelihood estimation problem. Further, we propose an algorithm framework, and
develop two first-order methods, that is, the adaptive spectral projected
gradient (ASPG) method and the adaptive Nesterov's smooth (ANS) method, for
solving this estimation problem. Finally, we compare the performance of these
two methods on a set of randomly generated instances. Our computational results
demonstrate that both methods are able to solve problems of size at least a
thousand and number of constraints of nearly a half million within a reasonable
amount of time, and the ASPG method generally outperforms the ANS method.Comment: 19 pages, 1 figur
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