IBM Research Report SINCO - A Greedy Coordinate Ascent Method for Sparse Inverse Covariance Selection Problem

In this paper, we consider the sparse inverse covariance selection problem which is equivalent to structure recovery of a Markov Network over Gaussian variables. We introduce a simple but efficient greedy algorithm, called SINCO, for solving the Sparse INverse COvariance problem. Our approach is based on coordinate ascent method which naturally preserves the sparsity of the inverse covariance matrix. We compare our algorithm to the state-of-art method called glasso [5], evaluating both computational efficiency and structure-reconstruction accuracy of both methods. We show that the two methods are often comparable in speed and accuracy, however, in some regimes, our method can significantly outperform glasso in terms of both computational time and structure reconstruction error (particularly, false positive error). Our method has an additional advantage of being easily parallelizable. We also show that the greedy nature of the method is such that one can reproduce the regularization path behavior by applying the method to one instance of the regularization parameter only. Numerical experiments demonstrate advantages of our approach on simulated networks, both random and “structured” (scale-free) ones, where the ground-truth structure is available. We also report promising empirical results on real-life problems with unknown ground-truth structure, such as classification of mental states from fMRI data.