Bayesian Joint Spike-and-Slab Graphical Lasso

Zehang Li, Tyler Mccormick, Samuel Clark
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:3877-3885, 2019.

Abstract

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently and automatically with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-li19h, title = {{B}ayesian Joint Spike-and-Slab Graphical Lasso}, author = {Li, Zehang and Mccormick, Tyler and Clark, Samuel}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {3877--3885}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/li19h/li19h.pdf}, url = {https://proceedings.mlr.press/v97/li19h.html}, abstract = {In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently and automatically with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.} }
Endnote
%0 Conference Paper %T Bayesian Joint Spike-and-Slab Graphical Lasso %A Zehang Li %A Tyler Mccormick %A Samuel Clark %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-li19h %I PMLR %P 3877--3885 %U https://proceedings.mlr.press/v97/li19h.html %V 97 %X In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently and automatically with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.
APA
Li, Z., Mccormick, T. & Clark, S.. (2019). Bayesian Joint Spike-and-Slab Graphical Lasso. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:3877-3885 Available from https://proceedings.mlr.press/v97/li19h.html.

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