Differentiable Compositional Kernel Learning for Gaussian Processes
This addresses the problem of kernel design for Gaussian processes, which is critical for practitioners in machine learning, but it is incremental as it builds on existing compositional kernel methods like the Automatic Statistician.
The paper tackles the challenge of kernel selection in Gaussian processes by introducing the Neural Kernel Network (NKN), a differentiable, neural network-based family of kernels that is universal for stationary kernels and demonstrates improved pattern discovery and extrapolation in tasks like time series and Bayesian optimization.
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.