GNet: A scalable and flexible Gaussian process network with nonparametric neurons

2026-07-12

AI Summary

This work addresses the high computational and memory costs of Gaussian processes in high-dimensional nonlinear prediction by proposing a Gaussian process network integrated with nonparametric activation functions. The method employs a unified optimization framework for flexible modeling and introduces a joint inverse Kalman filtering algorithm that avoids explicit construction of the covariance matrix while enabling closed-form gradient computation, thereby substantially reducing both time and space complexity. Empirical evaluations on nonlinear function approximation, nonparametric regression with real-world datasets, and high-dimensional density functional theory prediction demonstrate the model’s superior performance, confirming its efficiency and scalability.

Abstract

We develop GNet, a scalable and flexible Gaussian process network with nonparametric activation functions modeled by Gaussian processes. To reduce computational and storage costs, we introduce the jointly inverse Kalman filter, a fast algorithm together with closed-form expressions of gradients for accelerating model training and predictions without the need to form covariance matrices. Using a unified optimization setting, GNet shows competitive performance across a diverse range of test problems, including predicting nonlinear functions, nonparametric regression of real-world data, and predicting one-body direct correlation functions with high-dimensional inputs in classical density function theory. The strong performance of GNet, accelerated by the jointly inverse Kalman filter, suggests broad applicability to large-scale predictive modeling with substantially reduced computational and storage costs.

Problem

• Gaussian process
• scalable modeling
• computational cost
• nonparametric regression
• high-dimensional prediction

Innovation

• Gaussian process network
• nonparametric neurons
• jointly inverse Kalman filter
• scalable inference
• closed-form gradients