A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models

Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large K) under a high-dimensional (large p) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs rely on penalized log-likelihood estimators that involve expensive and difficult non-smooth optimizations. We propose a novel approach, FASJEM for underlinefast and underlinescalable underlinejoint structure-underlineestimation of underlinemultiple sGGMs at a large scale. As the first study of joint sGGM using the Elementary Estimator framework, our work has three major contributions: (1) We solve FASJEM through an entry-wise manner which is parallelizable. (2) We choose a proximal algorithm to optimize FASJEM. This improves the computational efficiency from O(Kp3) to O(Kp2) and reduces the memory requirement from O(Kp2) to O(K). (3) We theoretically prove that FASJEM achieves a consistent estimation with a convergence rate of O(log(Kp)/ntot). On several synthetic and four real-world datasets, FASJEM shows significant improvements over baselines on accuracy, computational complexity, and memory costs.