Gaussian Processes and Bayesian Inference
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Abstract
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.
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@article{Gu2026GNet,
title = {GNet: A scalable and flexible Gaussian process network with nonparametric neurons},
author = {Mengyang Gu},
journal = {arXiv (Cornell University)},
year = {2026},
doi = {10.48550/arxiv.2607.10735},
url = {https://doi.org/10.48550/arxiv.2607.10735}
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