Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908894174904320 |
|---|---|
| author | Williams, Bernardo Tetali, Harsha Vardhan Klami, Arto Hartmann, Marcelo |
| author_facet | Williams, Bernardo Tetali, Harsha Vardhan Klami, Arto Hartmann, Marcelo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Williams, Bernardo Tetali, Harsha Vardhan Klami, Arto Hartmann, Marcelo Machine Learning 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. |
| title | Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.16621 |