Two New Algorithms for Solving Covariance Graphical Lasso Based on Coordinate Descent and ECM
This work addresses a computational bottleneck for statisticians and data analysts using sparse covariance estimation, but it is incremental as it builds on prior algorithms.
The authors tackled the problem of solving the covariance graphical lasso by proposing two new algorithms based on coordinate descent and ECM, showing they outperform the existing method in simplicity, speed, and stability.
Covariance graphical lasso applies a lasso penalty on the elements of the covariance matrix. This method is useful because it not only produces sparse estimation of covariance matrix but also discovers marginal independence structures by generating zeros in the covariance matrix. We propose and explore two new algorithms for solving the covariance graphical lasso problem. Our new algorithms are based on coordinate descent and ECM. We show that these two algorithms are more attractive than the only existing competing algorithm of Bien and Tibshirani (2011) in terms of simplicity, speed and stability. We also discuss convergence properties of our algorithms.