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

Abstract

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 $O(K{p}^3)$ to $O(K{p}^2)$ and reduces the memory requirement from $O(K{p}^2)$ 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.

8 pages, accepted by AISTAT 2017

References in corpus (1)

• Consistency of objective Bayes factors as the model dimension grows

Cited by in corpus (3)

• Meta-modal Information Flow: A Method for Capturing Multimodal Modular Disconnectivity in Schizophrenia
• A Fast and Scalable Joint Estimator for Integrating Additional Knowledge in Learning Multiple Related Sparse Gaussian Graphical Models
• Methods for Recovering Conditional Independence Graphs: A Survey