Structural Kernel Search via Bayesian Optimization and Symbolical Optimal Transport

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. We propose measuring the distance between two kernels via their symbolical representation of their associated statistical hypothesis. We utilize the highly general kernel-grammar, presented in [3], as underlying kernel space, where each kernel is build from base kernels and operators, like e.g. LIN + ((SE × PER) + SE) 36th Conference on Neural Information Processing Systems (NeurIPS 2022).