Variable Clustering via Distributionally Robust Nodewise Regression

Kaizheng Wang, Xiao Xu, Xunyu Zhou
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:131553-131583, 2026.

Abstract

We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation, provide a data-driven approach for selecting the size of the robust region, and develop an ADMM algorithm for efficient implementation. We validate our method in extensive numerical studies and demonstrate its superior performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-wang26jk, title = {Variable Clustering via Distributionally Robust Nodewise Regression}, author = {Wang, Kaizheng and Xu, Xiao and Zhou, Xunyu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {131553--131583}, 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/wang26jk/wang26jk.pdf}, url = {https://proceedings.mlr.press/v306/wang26jk.html}, abstract = {We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation, provide a data-driven approach for selecting the size of the robust region, and develop an ADMM algorithm for efficient implementation. We validate our method in extensive numerical studies and demonstrate its superior performance.} }
Endnote
%0 Conference Paper %T Variable Clustering via Distributionally Robust Nodewise Regression %A Kaizheng Wang %A Xiao Xu %A Xunyu Zhou %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-wang26jk %I PMLR %P 131553--131583 %U https://proceedings.mlr.press/v306/wang26jk.html %V 306 %X We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation, provide a data-driven approach for selecting the size of the robust region, and develop an ADMM algorithm for efficient implementation. We validate our method in extensive numerical studies and demonstrate its superior performance.
APA
Wang, K., Xu, X. & Zhou, X.. (2026). Variable Clustering via Distributionally Robust Nodewise Regression. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:131553-131583 Available from https://proceedings.mlr.press/v306/wang26jk.html.

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