Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

By Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic, Bharath K. Sriperumbudur. arXiv.org, 2018

431 citations recorded by the source corpus.

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/71de5ab144545b697ccae97bc0a9dc67cb392cb2

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Citations in the corpus

On the Similarity between the Laplace and Neural Tangent Kernels (2020, background): “Kernels are mainly characterized by their corresponding Reproducing Kernel Hilbert Space (RKHS), which determines the set of functions they can produce [28].”
Locality defeats the curse of dimensionality in convolutional teacher–student scenarios (2021, background): “[29] Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic, and Bharath K Sriperumbudur.”