# Orthogonal Gaussian process models

arXiv: https://arxiv.org/abs/1611.00203 · HTML: https://mlsanity.com/paper/1611.00203/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2016.

## Built on by (most cited first, 10 of 10)

- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Additive Gaussian Processes Revisited](https://mlsanity.com/paper/2206.09861/) (2022)
- [LLaVA-FA: Learning Fourier Approximation for Compressing Large Multimodal Models](https://mlsanity.com/paper/2602.00135/) (2026)
- [A Kernel-Based Approach for Modelling Gaussian Processes with Functional Information](https://mlsanity.com/paper/2201.11023/) (2022)
- [Rational Kriging](https://mlsanity.com/paper/2312.05372/) (2023)
- [Deep P-Spline: Theory, Fast Tuning, and Application](https://mlsanity.com/paper/2501.01376/) (2025)
- [Effect Decomposition of Functional-Output Computer Experiments via Orthogonal Additive Gaussian Processes](https://mlsanity.com/paper/2506.12701/) (2025)
- [Sequential Adaptive Priors for Orthogonal Functions](https://mlsanity.com/paper/2508.15552/) (2025)
- [Orthogonal Discrepancy Kernels for Learning with Partial Physics](https://mlsanity.com/paper/2606.21199/) (2026)

## Abstract (arXiv)

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. This paper also discusses applications to multi-fidelity simulations using data examples.