17,529 research outputs found
High dimensional Sparse Gaussian Graphical Mixture Model
This paper considers the problem of networks reconstruction from
heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well
known that parameter estimation in this context is challenging due to large
numbers of variables coupled with the degeneracy of the likelihood. We propose
as a solution a penalized maximum likelihood technique by imposing an
penalty on the precision matrix. Our approach shrinks the parameters thereby
resulting in better identifiability and variable selection. We use the
Expectation Maximization (EM) algorithm which involves the graphical LASSO to
estimate the mixing coefficients and the precision matrices. We show that under
certain regularity conditions the Penalized Maximum Likelihood (PML) estimates
are consistent. We demonstrate the performance of the PML estimator through
simulations and we show the utility of our method for high dimensional data
analysis in a genomic application
A Low Density Lattice Decoder via Non-Parametric Belief Propagation
The recent work of Sommer, Feder and Shalvi presented a new family of codes
called low density lattice codes (LDLC) that can be decoded efficiently and
approach the capacity of the AWGN channel. A linear time iterative decoding
scheme which is based on a message-passing formulation on a factor graph is
given.
In the current work we report our theoretical findings regarding the relation
between the LDLC decoder and belief propagation. We show that the LDLC decoder
is an instance of non-parametric belief propagation and further connect it to
the Gaussian belief propagation algorithm. Our new results enable borrowing
knowledge from the non-parametric and Gaussian belief propagation domains into
the LDLC domain. Specifically, we give more general convergence conditions for
convergence of the LDLC decoder (under the same assumptions of the original
LDLC convergence analysis). We discuss how to extend the LDLC decoder from
Latin square to full rank, non-square matrices. We propose an efficient
construction of sparse generator matrix and its matching decoder. We report
preliminary experimental results which show our decoder has comparable symbol
to error rate compared to the original LDLC decoder.%Comment: Submitted for publicatio
Robust methods for inferring sparse network structures
This is the post-print version of the final paper published in Computational Statistics & Data Analysis. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2013 Elsevier B.V.Networks appear in many fields, from finance to medicine, engineering, biology and social science. They often comprise of a very large number of entities, the nodes, and the interest lies in inferring the interactions between these entities, the edges, from relatively limited data. If the underlying network of interactions is sparse, two main statistical approaches are used to retrieve such a structure: covariance modeling approaches with a penalty constraint that encourages sparsity of the network, and nodewise regression approaches with sparse regression methods applied at each node. In the presence of outliers or departures from normality, robust approaches have been developed which relax the assumption of normality. Robust covariance modeling approaches are reviewed and compared with novel nodewise approaches where robust methods are used at each node. For low-dimensional problems, classical deviance tests are also included and compared with penalized likelihood approaches. Overall, copula approaches are found to perform best: they are comparable to the other methods under an assumption of normality or mild departures from this, but they are superior to the other methods when the assumption of normality is strongly violated
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