Efficient and Accurate Inference for Matérn Gaussian Processes on Intervals

About

A new study by researchers at KAUST introduces a breakthrough method for statistical modeling with Matérn Gaussian processes, a popular tool in spatial statistics, machine learning, and the natural sciences. While Gaussian processes with stationary Matérn covariance functions (Matérn processes) are valued for their flexibility, their use with large datasets has been severely limited by the high computational cost of standard methods. 

The team has developed the first generally applicable approach that enables fast, linear-cost inference and prediction for Matérn processes on bounded intervals, without sacrificing accuracy. Their technique relies on a rational approximation that is not only efficient but also comes with theoretical guarantees: the approximation error in the covariance function decreases exponentially with the method’s complexity, allowing users to achieve high precision with minimal computational resources. 

Unlike most previous methods in the field, the new approach was developed with mathematical rigour and can be seamlessly integrated into general statistical software, such as R-INLA. It has also been empirically shown to outperform existing approaches in both accuracy and efficiency. This advance opens up new possibilities for researchers who rely on Matérn models in fields ranging from environmental modeling to machine learning.

The work is published in the prestigious Journal of Machine Learning Research, one of the very few journals that features mathematically rigorous results in machine learning. The method is implemented in the R package rSPDE. All code and further results are available on GitHub.

REFERENCE:

Bolin, D., Mehandiratta, V. and Simas, A. B. (2025). Linear cost and exponentially convergent approximation of Gaussian Matérn processes on intervals. Journal of Machine Learning Research, 26, 1–34.