Using the Equivalent Kernel to Understand Gaussian Process Regression

The equivalent kernel [1] is a way of understanding how Gaussian process regressionworks for large sample sizes based on a continuum limit. In this paper we show (1) how to approximate the equivalent kernel of the widely-used squared exponential (or Gaussian) kernel and related kernels, and(2) how analysis using the equivalent kernel helps to understand the learning curves for Gaussian processes.