Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian estimation of a sparse precision matrix   We consider the problem of estimating a sparse precision matrix of a
multivariate Gaussian distribution, including the case where the dimension $p$
is large. Gaussian graphical models provide an important tool in describing
conditional independence through presence or absence of the edges in the
underlying graph. A popular non-Bayesian method of estimating a graphical
structure is given by the graphical lasso. In this paper, we consider a
Bayesian approach to the problem. We use priors which put a mixture of a point
mass at zero and certain absolutely continuous distribution on off-diagonal
elements of the precision matrix. Hence the resulting posterior distribution
can be used for graphical structure learning. The posterior convergence rate of
the precision matrix is obtained. The posterior distribution on the model space
is extremely cumbersome to compute. We propose a fast computational method for
approximating the posterior probabilities of various graphs using the Laplace
approximation approach by expanding the posterior density around the posterior
mode, which is the graphical lasso by our choice of the prior distribution. We
also provide estimates of the accuracy in the approximation.

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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex