The Journal of Machine Learning Research
Learning sparse Gaussian Markov networks using a greedy coordinate ascent approach
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
Super-Linear Convergence of Dual Augmented Lagrangian Algorithm for Sparsity Regularized Estimation
The Journal of Machine Learning Research
Foundations and Trends® in Machine Learning
On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method
SIAM Journal on Numerical Analysis
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Sparse Inverse Covariance Selection (SICS) is a popular tool identifying an intrinsic relationship between continuous random variables. In this paper, we treat the extension of SICS to the grouped feature model in which the state-of-the-art SICS algorithm is no longer applicable. Such an extended model is essential when we aim to find a group-wise relationships between sets of variables, e.g. unknown interactions between groups of genes. We tackle the problem with a technique called Dual Augmented Lagrangian (DAL) that provides an efficient method for grouped sparse problems. We further improve the DAL framework by combining the Alternating Direction Method of Multipliers (ADMM), which dramatically simplifies the entire procedure of DAL and reduce the computational cost. We also provide empirical comparisons of the proposed DAL---ADMM algorithm against existing methods.