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 = {Beilun Wang and Ji Gao and Yanjun Qi}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {1168--1177}, year = {2017}, editor = {Aarti Singh and Jerry Zhu}, volume = {54}, series = {Proceedings of Machine Learning Research}, address = {Fort Lauderdale, FL, USA}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/wang17e/wang17e.pdf}, url = {http://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 %J Proceedings of Machine Learning Research %P 1168--1177 %U http://proceedings.mlr.press %V 54 %W PMLR %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 PMLR 54:1168-1177

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