Bayesian Joint Estimation of Multiple Graphical Models
Lingrui Gan, Xinming Yang, Naveen Narisetty, Feng Liang
Abstract
In this paper, we propose a novel Bayesian group regularization method based on the spike and slab Lasso priors for jointly estimating multiple graphical models. The proposed method can be used to estimate the common sparsity structure underlying the graphical models while capturing potential heterogeneity of the precision matrices corresponding to those models. Our theoretical results show that the proposed method enjoys the optimal rate of convergence in $\ell_\infty$ norm for estimation consistency and has a strong structure recovery guarantee even when the signal strengths over different graphs are heterogeneous. Through simulation studies and an application to the capital bike-sharing network data, we demonstrate the competitive performance of our method compared to existing alternatives.
BibTeX
@inproceedings{NEURIPS2019_94130ea1,
author = {Gan, Lingrui and Yang, Xinming and Narisetty, Naveen and Liang, Feng},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Bayesian Joint Estimation of Multiple Graphical Models},
url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/94130ea17023c4837f0dcdda95034b65-Paper.pdf},
volume = {32},
year = {2019}
}