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
\underline{fa}st and \underline{s}calable \underline{j}oint
structure-\underline{e}stimation of \underline{m}ultiple 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
$O(Kp^3)$ 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 estimation
with a convergence rate of $O(\log(Kp)/n_{tot})$. On several synthetic and four
real-world datasets, FASJEM shows significant improvements over baselines on
accuracy, computational complexity, and memory costs.

本文提出了一种基于 Elementary Estimator 框架的 proximal 算法 FASJEM，用于快速且可扩展地共同估计多个稀疏高斯图模型的结构，通过以 entry-wise 方式求解和优化，显著提高了精度、计算复杂度和内存利用率。