# Multi-Class Gaussian Process Classification Made Conjugate: Efficient Inference via Data Augmentation

arXiv: https://arxiv.org/abs/1905.09670 · HTML: https://mlsanity.com/paper/1905.09670/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 16 of 16)

- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning](https://mlsanity.com/paper/2102.07868/) (2021)
- [Multi-Instance Partial-Label Learning: Towards Exploiting Dual Inexact Supervision](https://mlsanity.com/paper/2212.08997/) (2022)
- [Adaptive Inducing Points Selection For Gaussian Processes](https://mlsanity.com/paper/2107.10066/) (2021)
- [Transductive Decoupled Variational Inference for Few-Shot Classification](https://mlsanity.com/paper/2208.10559/) (2022)
- [Scalable Cross Validation Losses for Gaussian Process Models](https://mlsanity.com/paper/2105.11535/) (2021)
- [Leveraging Instance Features for Label Aggregation in Programmatic Weak Supervision](https://mlsanity.com/paper/2210.02724/) (2022)
- [Revisiting Logistic-softmax Likelihood in Bayesian Meta-Learning for Few-Shot Classification](https://mlsanity.com/paper/2310.10379/) (2023)
- [Heterogeneous Multi-Task Gaussian Cox Processes](https://mlsanity.com/paper/2308.15364/) (2023)
- [Easy Variational Inference for Categorical Models via an Independent Binary Approximation](https://mlsanity.com/paper/2206.00093/) (2022)
- [Rethinking Approximate Gaussian Inference in Classification](https://mlsanity.com/paper/2502.03366/) (2025)
- [Accelerating Convergence in Bayesian Few-Shot Classification](https://mlsanity.com/paper/2405.01507/) (2024)
- [Task Diversity in Bayesian Federated Learning: Simultaneous Processing of Classification and Regression](https://mlsanity.com/paper/2412.10897/) (2024)
- [Few-Shot Speech Deepfake Detection Adaptation with Gaussian Processes](https://mlsanity.com/paper/2505.23619/) (2025)
- [On the Calibration and Uncertainty with P'olya-Gamma Augmentation for Dialog Retrieval Models](https://mlsanity.com/paper/2303.08606/) (2023)
- [Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification](https://mlsanity.com/paper/2603.16621/) (2026)

## Abstract (arXiv)

We propose a new scalable multi-class Gaussian process classification approach building on a novel modified softmax likelihood function. The new likelihood has two benefits: it leads to well-calibrated uncertainty estimates and allows for an efficient latent variable augmentation. The augmented model has the advantage that it is conditionally conjugate leading to a fast variational inference method via block coordinate ascent updates. Previous approaches suffered from a trade-off between uncertainty calibration and speed. Our experiments show that our method leads to well-calibrated uncertainty estimates and competitive predictive performance while being up to two orders faster than the state of the art.