# Deep Structured Mixtures of Gaussian Processes

arXiv: https://arxiv.org/abs/1910.04536 · HTML: https://mlsanity.com/paper/1910.04536/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2019.

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

- [Affective Processes: stochastic modelling of temporal context for emotion and facial expression recognition](https://mlsanity.com/paper/2103.13372/) (2021)
- [Incremental Ensemble Gaussian Processes](https://mlsanity.com/paper/2110.06777/) (2021)
- [Non-Gaussian Gaussian Processes for Few-Shot Regression](https://mlsanity.com/paper/2110.13561/) (2021)
- [Building Expressive and Tractable Probabilistic Generative Models: A Review](https://mlsanity.com/paper/2402.00759/) (2024)
- [Leveraging Probabilistic Circuits for Nonparametric Multi-Output Regression](https://mlsanity.com/paper/2106.08687/) (2021)
- [Characteristic Circuits](https://mlsanity.com/paper/2312.07790/) (2023)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Version](https://mlsanity.com/paper/2508.03679/) (2025)
- [Healing Products of Gaussian Processes](https://mlsanity.com/paper/2102.07106/) (2021)
- [Mixtures of Gaussian Processes for regression under multiple prior distributions](https://mlsanity.com/paper/2104.09185/) (2021)
- [Sum-Product-Attention Networks: Leveraging Self-Attention in Probabilistic Circuits](https://mlsanity.com/paper/2109.06587/) (2021)
- [Polynomial Chaos Expanded Gaussian Process](https://mlsanity.com/paper/2405.01052/) (2024)
- [RECOWNs: Probabilistic Circuits for Trustworthy Time Series Forecasting](https://mlsanity.com/paper/2106.04148/) (2021)
- [Reservoir History Matching of the Norne field with generative exotic priors and a coupled Mixture of Experts -- Physics Informed Neural Operator Forward Model](https://mlsanity.com/paper/2406.00889/) (2024)
- [SEEK: Self-adaptive Explainable Kernel For Nonstationary Gaussian Processes](https://mlsanity.com/paper/2503.14785/) (2025)

## Abstract (arXiv)

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is based on local GP experts. However, local-expert techniques proposed so far are either not well-principled, come with limited approximation guarantees, or lead to intractable models. In this paper, we introduce deep structured mixtures of GP experts, a stochastic process model which i) allows exact posterior inference, ii) has attractive computational and memory costs, and iii) when used as GP approximation, captures predictive uncertainties consistently better than previous expert-based approximations. In a variety of experiments, we show that deep structured mixtures have a low approximation error and often perform competitive or outperform prior work.