# Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation

arXiv: https://arxiv.org/abs/2101.09747 · HTML: https://mlsanity.com/paper/2101.09747/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 43 references that are in the map.
- First posted on arXiv 24 Jan 2021.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Towards new cross-validation-based estimators for Gaussian process regression: efficient adjoint computation of gradients](https://mlsanity.com/paper/2002.11543/) (2020)

## Built on by (most cited first, 7 of 7)

- [Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees](https://mlsanity.com/paper/2210.07893/) (2022)
- [Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning](https://mlsanity.com/paper/2203.02865/) (2022)
- [Nonparametric Multi-shape Modeling with Uncertainty Quantification](https://mlsanity.com/paper/2206.09127/) (2022)
- [A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling](https://mlsanity.com/paper/2305.10158/) (2023)
- [Rational kernel-based interpolation for complex-valued frequency response functions](https://mlsanity.com/paper/2307.13484/) (2023)
- [A class of modular and flexible covariate-based covariance functions for nonstationary spatial modeling](https://mlsanity.com/paper/2410.16716/) (2024)
- [Index-aware learning of circuits](https://mlsanity.com/paper/2309.00958/) (2023)

## Abstract (arXiv)

This article investigates the origin of numerical issues in maximum likelihood parameter estimation for Gaussian process (GP) interpolation and investigates simple but effective strategies for improving commonly used open-source software implementations. This work targets a basic problem but a host of studies, particularly in the literature of Bayesian optimization, rely on off-the-shelf GP implementations. For the conclusions of these studies to be reliable and reproducible, robust GP implementations are critical.