GLAD: Learning Sparse Graph Recovery
This work addresses a fundamental problem in machine learning for applications requiring sparse graph recovery, but it is incremental as it builds on existing optimization methods with a learned approach.
The authors tackled the problem of recovering sparse conditional independence graphs from data by proposing GLAD, a deep learning architecture that uses an Alternating Minimization algorithm as inductive bias and learns parameters via supervised learning, resulting in a compact and effective model.
Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex optimization algorithms have been designed to solve this formulation to recover the graph structure. Recently, there is a surge of interest to learn algorithms directly based on data, and in this case, learn to map empirical covariance to the sparse precision matrix. However, it is a challenging task in this case, since the symmetric positive definiteness (SPD) and sparsity of the matrix are not easy to enforce in learned algorithms, and a direct mapping from data to precision matrix may contain many parameters. We propose a deep learning architecture, GLAD, which uses an Alternating Minimization (AM) algorithm as our model inductive bias, and learns the model parameters via supervised learning. We show that GLAD learns a very compact and effective model for recovering sparse graphs from data.