Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process
This work addresses the problem of reliable probabilistic classification for machine learning practitioners, but it is incremental as it builds on existing GP and geometry-based methods.
The paper tackled multi-class classification by proposing a Gaussian process model that maps probability simplex values to Euclidean space using Aitchison geometry, resulting in conjugate inference and well-calibrated predictive probabilities without approximations, with empirical results showing competitive performance on synthetic and real-world datasets.
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.