Wasserstein Distributional Learning via Majorization-Minimization

Chengliang Tang, Nathan Lenssen, Ying Wei, Tian Zheng
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:10703-10731, 2023.

Abstract

Learning function-on-scalar predictive models for conditional densities and identifying factors that influence the entire probability distribution are vital tasks in many data-driven applications. We present an efficient Majorization-Minimization optimization algorithm, Wasserstein Distributional Learning (WDL), that trains Semi-parametric Conditional Gaussian Mixture Models (SCGMM) for conditional density functions and uses the Wasserstein distance $W_2$ as a proper metric for the space of density outcomes. We further provide theoretical convergence guarantees and illustrate the algorithm using boosted machines. Experiments on the synthetic data and real-world applications demonstrate the effectiveness of the proposed WDL algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-tang23b, title = {Wasserstein Distributional Learning via Majorization-Minimization}, author = {Tang, Chengliang and Lenssen, Nathan and Wei, Ying and Zheng, Tian}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {10703--10731}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/tang23b/tang23b.pdf}, url = {https://proceedings.mlr.press/v206/tang23b.html}, abstract = {Learning function-on-scalar predictive models for conditional densities and identifying factors that influence the entire probability distribution are vital tasks in many data-driven applications. We present an efficient Majorization-Minimization optimization algorithm, Wasserstein Distributional Learning (WDL), that trains Semi-parametric Conditional Gaussian Mixture Models (SCGMM) for conditional density functions and uses the Wasserstein distance $W_2$ as a proper metric for the space of density outcomes. We further provide theoretical convergence guarantees and illustrate the algorithm using boosted machines. Experiments on the synthetic data and real-world applications demonstrate the effectiveness of the proposed WDL algorithm.} }
Endnote
%0 Conference Paper %T Wasserstein Distributional Learning via Majorization-Minimization %A Chengliang Tang %A Nathan Lenssen %A Ying Wei %A Tian Zheng %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-tang23b %I PMLR %P 10703--10731 %U https://proceedings.mlr.press/v206/tang23b.html %V 206 %X Learning function-on-scalar predictive models for conditional densities and identifying factors that influence the entire probability distribution are vital tasks in many data-driven applications. We present an efficient Majorization-Minimization optimization algorithm, Wasserstein Distributional Learning (WDL), that trains Semi-parametric Conditional Gaussian Mixture Models (SCGMM) for conditional density functions and uses the Wasserstein distance $W_2$ as a proper metric for the space of density outcomes. We further provide theoretical convergence guarantees and illustrate the algorithm using boosted machines. Experiments on the synthetic data and real-world applications demonstrate the effectiveness of the proposed WDL algorithm.
APA
Tang, C., Lenssen, N., Wei, Y. & Zheng, T.. (2023). Wasserstein Distributional Learning via Majorization-Minimization. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:10703-10731 Available from https://proceedings.mlr.press/v206/tang23b.html.

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