The Log-Shift Penalty for Adaptive Estimation of Multiple Gaussian Graphical Models
Yuancheng Zhu, Rina Foygel Barber
Abstract
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model, which leads to an optimization problem with a nonconvex log-shift penalty function. We show that under mild conditions the optimization problem is convex despite the inclusion of a nonconvex penalty, and derive an efficient optimization algorithm. Experiments on both synthetic and real data show that the proposed method is able to achieve good selection and estimation performance simultaneously, because the nonconvexity of the log-shift penalty allows for weak signals to be thresholded to zero without excessive shrinkage on the strong signals.
BibTeX
@InProceedings{pmlr-v38-zhu15,
title = {{The Log-Shift Penalty for Adaptive Estimation of Multiple Gaussian Graphical Models}},
author = {Zhu, Yuancheng and Foygel Barber, Rina},
booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
pages = {1153--1161},
year = {2015},
editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
volume = {38},
series = {Proceedings of Machine Learning Research},
address = {San Diego, California, USA},
month = {09--12 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v38/zhu15.pdf},
url = {https://proceedings.mlr.press/v38/zhu15.html},
abstract = {Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model, which leads to an optimization problem with a nonconvex log-shift penalty function. We show that under mild conditions the optimization problem is convex despite the inclusion of a nonconvex penalty, and derive an efficient optimization algorithm. Experiments on both synthetic and real data show that the proposed method is able to achieve good selection and estimation performance simultaneously, because the nonconvexity of the log-shift penalty allows for weak signals to be thresholded to zero without excessive shrinkage on the strong signals.}
}