Heterogeneous Sufficient Dimension Reduction and Subspace Clustering

Lei Yan, Xin Zhang, Qing Mai
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:70330-70409, 2025.

Abstract

Scientific and engineering applications are often heterogeneous, making it beneficial to account for latent clusters or sub-populations when learning low-dimensional subspaces in supervised learning, and vice versa. In this paper, we combine the concept of subspace clustering with model-based sufficient dimension reduction and thus generalize the sufficient dimension reduction framework from homogeneous regression setting to heterogeneous data applications. In particular, we propose the mixture of principal fitted components (mixPFC) model, a novel framework that simultaneously achieves clustering, subspace estimation, and variable selection, providing a unified solution for high-dimensional heterogeneous data analysis. We develop a group Lasso penalized expectation-maximization (EM) algorithm and obtain its non-asymptotic convergence rate. Through extensive simulation studies, mixPFC demonstrates superior performance compared to existing methods across various settings. Applications to real world datasets further highlight its effectiveness and practical advantages.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-yan25e, title = {Heterogeneous Sufficient Dimension Reduction and Subspace Clustering}, author = {Yan, Lei and Zhang, Xin and Mai, Qing}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {70330--70409}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/yan25e/yan25e.pdf}, url = {https://proceedings.mlr.press/v267/yan25e.html}, abstract = {Scientific and engineering applications are often heterogeneous, making it beneficial to account for latent clusters or sub-populations when learning low-dimensional subspaces in supervised learning, and vice versa. In this paper, we combine the concept of subspace clustering with model-based sufficient dimension reduction and thus generalize the sufficient dimension reduction framework from homogeneous regression setting to heterogeneous data applications. In particular, we propose the mixture of principal fitted components (mixPFC) model, a novel framework that simultaneously achieves clustering, subspace estimation, and variable selection, providing a unified solution for high-dimensional heterogeneous data analysis. We develop a group Lasso penalized expectation-maximization (EM) algorithm and obtain its non-asymptotic convergence rate. Through extensive simulation studies, mixPFC demonstrates superior performance compared to existing methods across various settings. Applications to real world datasets further highlight its effectiveness and practical advantages.} }
Endnote
%0 Conference Paper %T Heterogeneous Sufficient Dimension Reduction and Subspace Clustering %A Lei Yan %A Xin Zhang %A Qing Mai %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-yan25e %I PMLR %P 70330--70409 %U https://proceedings.mlr.press/v267/yan25e.html %V 267 %X Scientific and engineering applications are often heterogeneous, making it beneficial to account for latent clusters or sub-populations when learning low-dimensional subspaces in supervised learning, and vice versa. In this paper, we combine the concept of subspace clustering with model-based sufficient dimension reduction and thus generalize the sufficient dimension reduction framework from homogeneous regression setting to heterogeneous data applications. In particular, we propose the mixture of principal fitted components (mixPFC) model, a novel framework that simultaneously achieves clustering, subspace estimation, and variable selection, providing a unified solution for high-dimensional heterogeneous data analysis. We develop a group Lasso penalized expectation-maximization (EM) algorithm and obtain its non-asymptotic convergence rate. Through extensive simulation studies, mixPFC demonstrates superior performance compared to existing methods across various settings. Applications to real world datasets further highlight its effectiveness and practical advantages.
APA
Yan, L., Zhang, X. & Mai, Q.. (2025). Heterogeneous Sufficient Dimension Reduction and Subspace Clustering. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:70330-70409 Available from https://proceedings.mlr.press/v267/yan25e.html.

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