Projected Subgradient Methods for Learning Sparse Gaussians
John Duchi, Stephen Gould, Daphne Koller
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 l1-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 l1-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.
PDF Link: /papers/08/p153-duchi.pdf
AUTHOR = "John Duchi
and Stephen Gould and Daphne Koller",
TITLE = "Projected Subgradient Methods for Learning Sparse Gaussians",
BOOKTITLE = "Proceedings of the Twenty-Fourth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-08)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2008",
PAGES = "153--160"