# Polynomial Chaos Expanded Gaussian Process

arXiv: https://arxiv.org/abs/2405.01052 · HTML: https://mlsanity.com/paper/2405.01052/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 2 May 2024.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Bayesian Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1905.03350/) (2019)
- [Polynomial-Chaos-based Kriging](https://mlsanity.com/paper/1502.03939/) (2015)
- [Deep Structured Mixtures of Gaussian Processes](https://mlsanity.com/paper/1910.04536/) (2019)
- [Variable selection for Gaussian processes via sensitivity analysis of the posterior predictive distribution](https://mlsanity.com/paper/1712.08048/) (2017)
- [Deep Gaussian Covariance Network](https://mlsanity.com/paper/1710.06202/) (2017)
- [Hierarchical-Hyperplane Kernels for Actively Learning Gaussian Process Models of Nonstationary Systems](https://mlsanity.com/paper/2303.10022/) (2023)

## Built on by (most cited first, 1 of 1)

- [Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions](https://mlsanity.com/paper/2409.12622/) (2024)

## Abstract (arXiv)

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning the experimental space and training multiple models, adding significant complexity. Recognizing this limitation, this study addresses the need for models that effectively represent both global and local experimental spaces. It introduces a novel machine learning (ML) approach: Polynomial Chaos Expanded Gaussian Process (PCEGP), leveraging polynomial chaos expansion (PCE) to calculate input-dependent hyperparameters of the Gaussian process (GP). This provides a mathematically interpretable approach that incorporates non-stationary covariance functions and heteroscedastic noise estimation to generate locally adapted models. The model performance is compared to different algorithms in benchmark tests for regression tasks. The results demonstrate low prediction errors of the PCEGP, highlighting model performance that is often competitive with or better than previous methods. A key advantage of the presented model is its interpretable hyperparameters along with training and prediction runtimes comparable to those of a GP.