Sparse Inverse Covariance Selection via Alternating Linearization Methods

Details Sparse Inverse Covariance Selection via Alternating Linearization Methods Sparse Inverse Covariance Selection via Alternating Linearization Methods

2010-10-30

arxiv.org/abs/1011.0097v1

NIPS 2010

Computer Science

Learning

Scientific paper

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 $\ell_1$-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 $\epsilon$-optimal solution in $O(1/\epsilon)$ 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.

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