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.
@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.}
}
%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.
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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