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Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for manyrelated tasks (large $K$) under a high-dimensional (large $p$) situation is animportant task. Most previous studies for the joint estimation of multiplesGGMs rely on penalized log-likelihood estimators that involve expensive anddifficult non-smooth optimizations. We propose a novel approach, FASJEM for\underline{fa}st and \underline{s}calable \underline{j}ointstructure-\underline{e}stimation of \underline{m}ultiple sGGMs at a largescale. As the first study of joint sGGM using the Elementary Estimatorframework, our work has three major contributions: (1) We solve FASJEM throughan entry-wise manner which is parallelizable. (2) We choose a proximalalgorithm to optimize FASJEM. This improves the computational efficiency from$O(Kp^3)$ to $O(Kp^2)$ and reduces the memory requirement from $O(Kp^2)$ to$O(K)$. (3) We theoretically prove that FASJEM achieves a consistent estimationwith a convergence rate of $O(\log(Kp)/n_{tot})$. On several synthetic and fourreal-world datasets, FASJEM shows significant improvements over baselines onaccuracy, computational complexity, and memory costs.

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