Projected Subgradient Methods for Learning Sparse Gaussians

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the 1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster than previous methods in practice and equal to the best performing of these in asymptotic complexity. We also extend the 1-regularized objective to the problem of sparsifying entire blocks within the inverse covariance matrix. Our methods generalize fairly easily to this case, while other methods do not. We demonstrate that our extensions give better generalization performance on two real domains--biological network analysis and a 2D-shape modeling image task.

• Type: Conference
• Year: 2008
• Where: UAI
• Authors: John Duchi, Stephen Gould, Daphne Koller
• Keywords: Artificial Intelligence, Better Generalization Performance, Inverse Covariance Matrix, Markov Random Fields, UAI 2008