# Healing Products of Gaussian Processes

arXiv: https://arxiv.org/abs/2102.07106 · HTML: https://mlsanity.com/paper/2102.07106/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 14 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1806.00720/) (2018)
- [Distributed Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models](https://mlsanity.com/paper/1402.1389/) (2014)
- [Nested Kriging predictions for datasets with large number of observations](https://mlsanity.com/paper/1607.05432/) (2016)
- [Deep Structured Mixtures of Gaussian Processes](https://mlsanity.com/paper/1910.04536/) (2019)
- [Embarrassingly Parallel Inference for Gaussian Processes](https://mlsanity.com/paper/1702.08420/) (2017)
- [Accelerating the BSM interpretation of LHC data with machine learning](https://mlsanity.com/paper/1611.02704/) (2016)
- [Transductive Log Opinion Pool of Gaussian Process Experts](https://mlsanity.com/paper/1511.07551/) (2015)

## Built on by (most cited first, 2 of 2)

- [When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Models](https://mlsanity.com/paper/2601.11444/) (2026)
- [Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Means](https://mlsanity.com/paper/2603.04204/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification.