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

Beilun Wang, Ji Gao, Yanjun Qi
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:1168-1177, 2017.

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 \underlinefast and \underlinescalable \underlinejoint structure-\underlineestimation of \underlinemultiple sGGMs at a large scale. As the first study of joint sGGM using the M-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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-wang17e, title = {{A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models}}, author = {Wang, Beilun and Gao, Ji and Qi, Yanjun}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {1168--1177}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/wang17e/wang17e.pdf}, url = {https://proceedings.mlr.press/v54/wang17e.html}, 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 \underlinefast and \underlinescalable \underlinejoint structure-\underlineestimation of \underlinemultiple sGGMs at a large scale. As the first study of joint sGGM using the M-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.} }
Endnote
%0 Conference Paper %T A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models %A Beilun Wang %A Ji Gao %A Yanjun Qi %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-wang17e %I PMLR %P 1168--1177 %U https://proceedings.mlr.press/v54/wang17e.html %V 54 %X 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 \underlinefast and \underlinescalable \underlinejoint structure-\underlineestimation of \underlinemultiple sGGMs at a large scale. As the first study of joint sGGM using the M-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.
APA
Wang, B., Gao, J. & Qi, Y.. (2017). A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:1168-1177 Available from https://proceedings.mlr.press/v54/wang17e.html.

Related Material