A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models
This work addresses a computational bottleneck in statistical learning for multi-task graphical model estimation, offering a scalable solution for large-scale applications.
The paper tackles the problem of jointly estimating multiple sparse Gaussian Graphical Models (sGGMs) for many related tasks under high-dimensional settings, proposing FASJEM, which improves computational efficiency from O(Kp^3) to O(Kp^2) and reduces memory requirements from O(Kp^2) to O(K), while achieving consistent estimation with a convergence rate of O(log(Kp)/n_tot).
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.