# Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions

arXiv: https://arxiv.org/abs/1410.7827 · HTML: https://mlsanity.com/paper/1410.7827/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2014.

## Built on by (most cited first, 30 of 67)

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- [Federated Bayesian Neural Regression: A Scalable Global Federated Gaussian Process](https://mlsanity.com/paper/2206.06357/) (2022)
- [Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regression](https://mlsanity.com/paper/2306.14731/) (2023)
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- [Learning Intuitive Physics with Multimodal Generative Models](https://mlsanity.com/paper/2101.04454/) (2021)
- [Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning](https://mlsanity.com/paper/2203.02865/) (2022)
- [Learning Sequential Latent Variable Models from Multimodal Time Series Data](https://mlsanity.com/paper/2204.10419/) (2022)
- [Generalized Product-of-Experts for Learning Multimodal Representations in Noisy Environments](https://mlsanity.com/paper/2211.03587/) (2022)
- [Unite and Conquer: Plug & Play Multi-Modal Synthesis using Diffusion Models](https://mlsanity.com/paper/2212.00793/) (2022)
- [Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Version](https://mlsanity.com/paper/2508.03679/) (2025)
- [Encoding Domain Knowledge in Multi-view Latent Variable Models: A Bayesian Approach with Structured Sparsity](https://mlsanity.com/paper/2204.06242/) (2022)
- [Multi-view Multi-label Fine-grained Emotion Decoding from Human Brain Activity](https://mlsanity.com/paper/2211.02629/) (2022)
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- [Vecchia Gaussian Process Ensembles on Internal Representations of Deep Neural Networks](https://mlsanity.com/paper/2305.17063/) (2023)
- [Learning-based Control for PMSM Using Distributed Gaussian Processes with Optimal Aggregation Strategy](https://mlsanity.com/paper/2307.13945/) (2023)

## Abstract (arXiv)

In this work, we propose a generalized product of experts (gPoE) framework for combining the predictions of multiple probabilistic models. We identify four desirable properties that are important for scalability, expressiveness and robustness, when learning and inferring with a combination of multiple models. Through analysis and experiments, we show that gPoE of Gaussian processes (GP) have these qualities, while no other existing combination schemes satisfy all of them at the same time. The resulting GP-gPoE is highly scalable as individual GP experts can be independently learned in parallel; very expressive as the way experts are combined depends on the input rather than fixed; the combined prediction is still a valid probabilistic model with natural interpretation; and finally robust to unreliable predictions from individual experts.