Graph Neural Network-Inspired Kernels for Gaussian Processes in Semi-Supervised LearningDownload PDF

Published: 01 Feb 2023, Last Modified: 17 Sept 2023ICLR 2023 posterReaders: Everyone
Keywords: graph neural network, Gaussian process, semi-supervised learning
TL;DR: Graph-based Gaussian process kernels are developed based on graph neural networks, showing competitive semi-supervised learning performance and timing advantage.
Abstract: Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a promising class of models for graph-structured data in semi-supervised learning and beyond. Their competitive performance is often attributed to a proper capturing of the graph inductive bias. In this work, we introduce this inductive bias into GPs to improve their predictive performance for graph-structured data. We show that a prominent example of GNNs, the graph convolutional network, is equivalent to some GP when its layers are infinitely wide; and we analyze the kernel universality and the limiting behavior in depth. We further present a programmable procedure to compose covariance kernels inspired by this equivalence and derive example kernels corresponding to several interesting members of the GNN family. We also propose a computationally efficient approximation of the covariance matrix for scalable posterior inference with large-scale data. We demonstrate that these graph-based kernels lead to competitive classification and regression performance, as well as advantages in computation time, compared with the respective GNNs.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: Probabilistic Methods (eg, variational inference, causal inference, Gaussian processes)
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 1 code implementation](
14 Replies