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A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models
Beilun Wang, Ji Gao, Yanjun Qi
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(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.
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