The Log-Shift Penalty for Adaptive Estimation of Multiple Gaussian Graphical Models

Yuancheng Zhu, Rina Foygel Barber
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:1153-1161, 2015.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T The Log-Shift Penalty for Adaptive Estimation of Multiple Gaussian Graphical Models %A Yuancheng Zhu %A Rina Foygel Barber %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-zhu15 %I PMLR %P 1153--1161 %U https://proceedings.mlr.press/v38/zhu15.html %V 38 %X 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.
RIS
TY - CPAPER TI - The Log-Shift Penalty for Adaptive Estimation of Multiple Gaussian Graphical Models AU - Yuancheng Zhu AU - Rina Foygel Barber BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-zhu15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 1153 EP - 1161 L1 - http://proceedings.mlr.press/v38/zhu15.pdf UR - https://proceedings.mlr.press/v38/zhu15.html AB - 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. ER -
APA
Zhu, Y. & Foygel Barber, R.. (2015). The Log-Shift Penalty for Adaptive Estimation of Multiple Gaussian Graphical Models. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:1153-1161 Available from https://proceedings.mlr.press/v38/zhu15.html.

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