# Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inference

arXiv: https://arxiv.org/abs/2107.12797 · HTML: https://mlsanity.com/paper/2107.12797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Streaming Variational Bayes](https://mlsanity.com/paper/1307.6769/) (2013)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Non-Stationary Spectral Kernels](https://mlsanity.com/paper/1705.08736/) (2017)
- [Deep convolutional Gaussian processes](https://mlsanity.com/paper/1810.03052/) (2018)
- [Consistent Online Gaussian Process Regression Without the Sample Complexity Bottleneck](https://mlsanity.com/paper/2004.11094/) (2020)
- [Bayesian Learning from Sequential Data using Gaussian Processes with Signature Covariances](https://mlsanity.com/paper/1906.08215/) (2019)

## Abstract (arXiv)

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data.