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Scalable L\'evy Process Priors for Spectral Kernel Learning by Jang, Phillip A.; Loeb, Andrew E.; Davidow, Matthew B.; Wilson, Andrew Gordon is a scholarly article available to read on EtoBox.

What is Scalable L\'evy Process Priors for Spectral Kernel Learning about?

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a L\'evy process. The resulting distribution has support for all stationary covariances--including the popular RBF, periodic, and Mat\'ern kernels--combined with inductive biases which enable automatic and data efficient learning, long-range extrapolation, and state of the art predictive performance. The proposed model also presents an approach to spectral regularization, as the L\'evy process introduces a sparsity-inducing prior over mixture components, allowing automatic selection over model order and pruning of extraneous components. We exploit the algebraic structure of the proposed process for $\mathcal{O}(n)$ training and $\mathcal{O}(1)$ predictions. We perform extrapolations having reasonable uncertainty estimates on several benchmarks, show that the proposed mo

Author

Jang, Phillip A.; Loeb, Andrew E.; Davidow, Matthew B.; Wilson, Andrew Gordon

Published

2018

Language

EN