# Approximate Inference for Nonstationary Heteroscedastic Gaussian process Regression

arXiv: https://arxiv.org/abs/1404.5443 · HTML: https://mlsanity.com/paper/1404.5443/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2014.

## Built on by (most cited first, 6 of 6)

- [Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees](https://mlsanity.com/paper/2111.01721/) (2021)
- [Sparse Algorithms for Markovian Gaussian Processes](https://mlsanity.com/paper/2103.10710/) (2021)
- [Active learning-assisted neutron spectroscopy with log-Gaussian processes](https://mlsanity.com/paper/2209.00980/) (2022)
- [Uncertainty Disentanglement with Non-stationary Heteroscedastic Gaussian Processes for Active Learning](https://mlsanity.com/paper/2210.10964/) (2022)
- [Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions](https://mlsanity.com/paper/2510.21974/) (2025)
- [A Framework for Nonstationary Gaussian Processes with Neural Network Parameters](https://mlsanity.com/paper/2507.12262/) (2025)

## Abstract (arXiv)

This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over input dependent noise variance (heteroscedasticity) and input dependent signal variance (nonstationarity) by setting independent GP priors for the noise and signal variances. We use expectation propagation (EP) for inference and compare results to Markov chain Monte Carlo in two simulated data sets and three empirical examples. The results show that EP produces comparable results with less computational burden.