Learning Mixtures of Gaussian Processes through Random Projection

Emmanuel Akeweje, Mimi Zhang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:720-739, 2024.

Abstract

We propose an ensemble clustering framework to uncover latent cluster labels in functional data generated from a Gaussian process mixture. Our method exploits the fact that the projection coefficients of the functional data onto any given projection function follow a univariate Gaussian mixture model (GMM). By conducting multiple one-dimensional projections and learning a univariate GMM for each, we create an ensemble of GMMs. Each GMM serves as a base clustering, and applying ensemble clustering yields a consensus clustering. Our approach significantly reduces computational complexity compared to state-of-the-art methods, and we provide theoretical guarantees on the identifiability and learnability of Gaussian process mixtures. Extensive experiments on synthetic and real datasets confirm the superiority of our method over existing techniques.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-akeweje24a, title = {Learning Mixtures of {G}aussian Processes through Random Projection}, author = {Akeweje, Emmanuel and Zhang, Mimi}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {720--739}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/akeweje24a/akeweje24a.pdf}, url = {https://proceedings.mlr.press/v235/akeweje24a.html}, abstract = {We propose an ensemble clustering framework to uncover latent cluster labels in functional data generated from a Gaussian process mixture. Our method exploits the fact that the projection coefficients of the functional data onto any given projection function follow a univariate Gaussian mixture model (GMM). By conducting multiple one-dimensional projections and learning a univariate GMM for each, we create an ensemble of GMMs. Each GMM serves as a base clustering, and applying ensemble clustering yields a consensus clustering. Our approach significantly reduces computational complexity compared to state-of-the-art methods, and we provide theoretical guarantees on the identifiability and learnability of Gaussian process mixtures. Extensive experiments on synthetic and real datasets confirm the superiority of our method over existing techniques.} }
Endnote
%0 Conference Paper %T Learning Mixtures of Gaussian Processes through Random Projection %A Emmanuel Akeweje %A Mimi Zhang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-akeweje24a %I PMLR %P 720--739 %U https://proceedings.mlr.press/v235/akeweje24a.html %V 235 %X We propose an ensemble clustering framework to uncover latent cluster labels in functional data generated from a Gaussian process mixture. Our method exploits the fact that the projection coefficients of the functional data onto any given projection function follow a univariate Gaussian mixture model (GMM). By conducting multiple one-dimensional projections and learning a univariate GMM for each, we create an ensemble of GMMs. Each GMM serves as a base clustering, and applying ensemble clustering yields a consensus clustering. Our approach significantly reduces computational complexity compared to state-of-the-art methods, and we provide theoretical guarantees on the identifiability and learnability of Gaussian process mixtures. Extensive experiments on synthetic and real datasets confirm the superiority of our method over existing techniques.
APA
Akeweje, E. & Zhang, M.. (2024). Learning Mixtures of Gaussian Processes through Random Projection. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:720-739 Available from https://proceedings.mlr.press/v235/akeweje24a.html.

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