Structural Kernel Search via Bayesian Optimization and Symbolical Optimal TransportDownload PDF

Published: 31 Oct 2022, Last Modified: 15 Dec 2022NeurIPS 2022 AcceptReaders: Everyone
Keywords: Bayesian Optimization, Gaussian Process, Kernel Search, Kernel
TL;DR: We propose a new method for kernel selection for Gaussian processes, where the distance between two GPs is measured using their associated symbolic description of the statistical hypothesis.
Abstract: Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert. Additionally, evaluating the model selection criteria for Gaussian processes typically scales cubically in the sample size, rendering kernel search particularly computationally expensive. We propose a novel, efficient search method through a general, structured kernel space. Previous methods solved this task via Bayesian optimization and relied on measuring the distance between GP's directly in function space to construct a kernel-kernel. We present an alternative approach by defining a kernel-kernel over the symbolic representation of the statistical hypothesis that is associated with a kernel. We empirically show that this leads to a computationally more efficient way of searching through a discrete kernel space.
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