Identifying Common Hubs in Multiple Gaussian Graphical Models

José Á Sánchez Gómez, Weibin Mo, Junlong Zhao, Yufeng Liu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:35811-35835, 2026.

Abstract

The Gaussian graphical model (GGM) is a useful tool to represent relationships of conditional dependence among variables. In many real-world applications, datasets often contain multiple related sub-populations, whose associated GGMs may have common structure, as well as large structural differences. In such cases, it is useful to recover common hub variables, which are the highly connected variables in the GGMs of all sub-populations. In this paper, we propose the Joint Inverse Components for Hub Detection (JIC-HD) method to recover the common hubs across multiple GGMs without the need to estimate all subpopulation GGMs. To this end, we introduce joint minimax eigenspaces, and show that these can be leveraged for the recovery of common hubs. We establish theoretical guarantees for the recovery of common hubs. Additionally, our numerical simulation studies confirm superior performance of our JIC-HD in detecting common hubs compared to the existing methods in the literature. Our method is especially advantageous when the multiple GGMs have both common and individual hubs across sub-populations. Finally, we analyze cancer gene-expression datasets and identify biologically meaningful common hub genes across cancer subtypes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-gomez26a, title = {Identifying Common Hubs in Multiple {G}aussian Graphical Models}, author = {G\'{o}mez, Jos\'{e} \'{A} S\'{a}nchez and Mo, Weibin and Zhao, Junlong and Liu, Yufeng}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {35811--35835}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/gomez26a/gomez26a.pdf}, url = {https://proceedings.mlr.press/v306/gomez26a.html}, abstract = {The Gaussian graphical model (GGM) is a useful tool to represent relationships of conditional dependence among variables. In many real-world applications, datasets often contain multiple related sub-populations, whose associated GGMs may have common structure, as well as large structural differences. In such cases, it is useful to recover common hub variables, which are the highly connected variables in the GGMs of all sub-populations. In this paper, we propose the Joint Inverse Components for Hub Detection (JIC-HD) method to recover the common hubs across multiple GGMs without the need to estimate all subpopulation GGMs. To this end, we introduce joint minimax eigenspaces, and show that these can be leveraged for the recovery of common hubs. We establish theoretical guarantees for the recovery of common hubs. Additionally, our numerical simulation studies confirm superior performance of our JIC-HD in detecting common hubs compared to the existing methods in the literature. Our method is especially advantageous when the multiple GGMs have both common and individual hubs across sub-populations. Finally, we analyze cancer gene-expression datasets and identify biologically meaningful common hub genes across cancer subtypes.} }
Endnote
%0 Conference Paper %T Identifying Common Hubs in Multiple Gaussian Graphical Models %A José Á Sánchez Gómez %A Weibin Mo %A Junlong Zhao %A Yufeng Liu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-gomez26a %I PMLR %P 35811--35835 %U https://proceedings.mlr.press/v306/gomez26a.html %V 306 %X The Gaussian graphical model (GGM) is a useful tool to represent relationships of conditional dependence among variables. In many real-world applications, datasets often contain multiple related sub-populations, whose associated GGMs may have common structure, as well as large structural differences. In such cases, it is useful to recover common hub variables, which are the highly connected variables in the GGMs of all sub-populations. In this paper, we propose the Joint Inverse Components for Hub Detection (JIC-HD) method to recover the common hubs across multiple GGMs without the need to estimate all subpopulation GGMs. To this end, we introduce joint minimax eigenspaces, and show that these can be leveraged for the recovery of common hubs. We establish theoretical guarantees for the recovery of common hubs. Additionally, our numerical simulation studies confirm superior performance of our JIC-HD in detecting common hubs compared to the existing methods in the literature. Our method is especially advantageous when the multiple GGMs have both common and individual hubs across sub-populations. Finally, we analyze cancer gene-expression datasets and identify biologically meaningful common hub genes across cancer subtypes.
APA
Gómez, J.Á.S., Mo, W., Zhao, J. & Liu, Y.. (2026). Identifying Common Hubs in Multiple Gaussian Graphical Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:35811-35835 Available from https://proceedings.mlr.press/v306/gomez26a.html.

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