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This research introduces a novel Gaussian process framework for multiclass classification by leveraging Aitchison geometry to map probability simplices into unconstrained Euclidean spaces. The approach enables conjugate inference with scalable sparse regression, offering well-calibrated predictions that avoid heavy distributional approximations common in standard models. By reducing latent dimensions while maintaining accuracy, this method advances the theoretical and practical efficiency of Bayesian machine learning for complex classification tasks.
Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification
arXiv:2603.16621v2 Announce Type: replace 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.
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.
Machine Learning (cs.LG)
arXiv:2603.16621 [cs.LG]
(or arXiv:2603.16621v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.16621 Focus to learn more arXiv-issued DOI via DataCite
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