Asymptotic Bayes risk of semi-supervised multitask learning on Gaussian mixture

Minh-Toan Nguyen, Romain Couillet
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:5063-5078, 2023.

Abstract

The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from which we analyze the role of task similarity in learning and evaluate the performance gain when tasks are learned together rather than separately. In the supervised case, we derive a simple algorithm that attains the Bayes optimal performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-nguyen23c, title = {Asymptotic Bayes risk of semi-supervised multitask learning on Gaussian mixture}, author = {Nguyen, Minh-Toan and Couillet, Romain}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {5063--5078}, 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/nguyen23c/nguyen23c.pdf}, url = {https://proceedings.mlr.press/v206/nguyen23c.html}, abstract = {The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from which we analyze the role of task similarity in learning and evaluate the performance gain when tasks are learned together rather than separately. In the supervised case, we derive a simple algorithm that attains the Bayes optimal performance.} }
Endnote
%0 Conference Paper %T Asymptotic Bayes risk of semi-supervised multitask learning on Gaussian mixture %A Minh-Toan Nguyen %A Romain Couillet %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-nguyen23c %I PMLR %P 5063--5078 %U https://proceedings.mlr.press/v206/nguyen23c.html %V 206 %X The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from which we analyze the role of task similarity in learning and evaluate the performance gain when tasks are learned together rather than separately. In the supervised case, we derive a simple algorithm that attains the Bayes optimal performance.
APA
Nguyen, M. & Couillet, R.. (2023). Asymptotic Bayes risk of semi-supervised multitask learning on Gaussian mixture. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:5063-5078 Available from https://proceedings.mlr.press/v206/nguyen23c.html.

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