Differentiable Compositional Kernel Learning for Gaussian Processes

TL;DR

This paper introduces the Neural Kernel Network (NKN), a differentiable, neural network-based approach for learning Gaussian process kernels that can approximate complex compositional structures and improve pattern discovery and extrapolation.

Contribution

The paper proposes NKN, a novel neural network architecture for kernel learning that is universal for stationary kernels and end-to-end trainable, enabling better kernel selection and structure discovery.

Findings

NKN can approximate compositional kernels used in automatic statistician.

NKN demonstrates superior pattern discovery in time series and textures.

NKN improves extrapolation and Bayesian optimization tasks.

Abstract

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The NKN architecture is based on the composition rules for kernels, so that each unit of the network corresponds to a valid kernel. It can compactly approximate compositional kernel structures such as those used by the Automatic Statistician (Lloyd et al., 2014), but because the architecture is differentiable, it is end-to-end trainable with gradient-based optimization. We show that the NKN is universal for the class of stationary kernels. Empirically we demonstrate pattern discovery and extrapolation abilities of NKN on several tasks that depend crucially on identifying the underlying structure, including time series and texture extrapolation, as well as Bayesian optimization.