Closed-Form Coordinate Ascent Variational Inference for Student-t Process Regression with Student-t Likelihood

Keisuke Onoue, Takatomi Kubo, Kazushi Ikeda
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1756-1764, 2026.

Abstract

Combining a Student-t Process prior with a Student-t likelihood yields a doubly robust regression model whose intractable posterior has prevented its practical use. We introduce the first tractable variational inference framework for this model. Leveraging the Student-t distribution’s scale-mixture representation, we design a structured variational family that affords an analytic evidence lower bound. To overcome the non-conjugacy of this family, which precludes closed-form updates, we devise a novel projection-based optimization: we find the optimum in a simpler, factorized family and analytically project it back onto our structured one. The framework is extended to a scalable sparse, stochastic setting. Empirical results demonstrate strong performance, particularly in the full-batch setting, establishing this robust model as a practical and powerful tool.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-onoue26a, title = { Closed-Form Coordinate Ascent Variational Inference for Student-t Process Regression with Student-t Likelihood }, author = {Onoue, Keisuke and Kubo, Takatomi and Ikeda, Kazushi}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1756--1764}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/onoue26a/onoue26a.pdf}, url = {https://proceedings.mlr.press/v300/onoue26a.html}, abstract = { Combining a Student-t Process prior with a Student-t likelihood yields a doubly robust regression model whose intractable posterior has prevented its practical use. We introduce the first tractable variational inference framework for this model. Leveraging the Student-t distribution’s scale-mixture representation, we design a structured variational family that affords an analytic evidence lower bound. To overcome the non-conjugacy of this family, which precludes closed-form updates, we devise a novel projection-based optimization: we find the optimum in a simpler, factorized family and analytically project it back onto our structured one. The framework is extended to a scalable sparse, stochastic setting. Empirical results demonstrate strong performance, particularly in the full-batch setting, establishing this robust model as a practical and powerful tool. } }
Endnote
%0 Conference Paper %T Closed-Form Coordinate Ascent Variational Inference for Student-t Process Regression with Student-t Likelihood %A Keisuke Onoue %A Takatomi Kubo %A Kazushi Ikeda %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-onoue26a %I PMLR %P 1756--1764 %U https://proceedings.mlr.press/v300/onoue26a.html %V 300 %X Combining a Student-t Process prior with a Student-t likelihood yields a doubly robust regression model whose intractable posterior has prevented its practical use. We introduce the first tractable variational inference framework for this model. Leveraging the Student-t distribution’s scale-mixture representation, we design a structured variational family that affords an analytic evidence lower bound. To overcome the non-conjugacy of this family, which precludes closed-form updates, we devise a novel projection-based optimization: we find the optimum in a simpler, factorized family and analytically project it back onto our structured one. The framework is extended to a scalable sparse, stochastic setting. Empirical results demonstrate strong performance, particularly in the full-batch setting, establishing this robust model as a practical and powerful tool.
APA
Onoue, K., Kubo, T. & Ikeda, K.. (2026). Closed-Form Coordinate Ascent Variational Inference for Student-t Process Regression with Student-t Likelihood . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1756-1764 Available from https://proceedings.mlr.press/v300/onoue26a.html.

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