Function-Space Distributions over Kernels
This work addresses representation learning and predictive performance in Gaussian processes for researchers and practitioners, offering a novel method for kernel learning without manual intervention.
The paper tackles the problem of learning covariance kernels in Gaussian processes by introducing functional kernel learning (FKL), which infers functional posteriors over kernels using a transformed Gaussian process over spectral densities, resulting in improved predictive performance and kernel recovery in various settings.
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop functional kernel learning (FKL) to directly infer functional posteriors over kernels. In particular, we place a transformed Gaussian process over a spectral density, to induce a non-parametric distribution over kernel functions. The resulting approach enables learning of rich representations, with support for any stationary kernel, uncertainty over the values of the kernel, and an interpretable specification of a prior directly over kernels, without requiring sophisticated initialization or manual intervention. We perform inference through elliptical slice sampling, which is especially well suited to marginalizing posteriors with the strongly correlated priors typical to function space modelling. We develop our approach for non-uniform, large-scale, multi-task, and multidimensional data, and show promising performance in a wide range of settings, including interpolation, extrapolation, and kernel recovery experiments.