Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification

Bernardo Williams, Harsha Vardhan Tetali, Arto Klami, Marcelo Hartmann
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:7370-7386, 2026.

Abstract

We propose a conjugate and calibrated {Gaussian} process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained {Euclidean} representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-williams26a, title = {Simplex-to-{Euclidean} Bijection for Conjugate and Calibrated Multiclass {Gaussian} Process Classification}, author = {Williams, Bernardo and Tetali, Harsha Vardhan and Klami, Arto and Hartmann, Marcelo}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {7370--7386}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/williams26a/williams26a.pdf}, url = {https://proceedings.mlr.press/v337/williams26a.html}, abstract = {We propose a conjugate and calibrated {Gaussian} process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained {Euclidean} representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification %A Bernardo Williams %A Harsha Vardhan Tetali %A Arto Klami %A Marcelo Hartmann %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-williams26a %I PMLR %P 7370--7386 %U https://proceedings.mlr.press/v337/williams26a.html %V 337 %X We propose a conjugate and calibrated {Gaussian} process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained {Euclidean} representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.
APA
Williams, B., Tetali, H.V., Klami, A. & Hartmann, M.. (2026). Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:7370-7386 Available from https://proceedings.mlr.press/v337/williams26a.html.

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