Understanding gaussian process regression using the equivalent kernel

The equivalent kernel [1] is a way of understanding how Gaussian process regression works for large sample sizes based on a con- tinuum limit. In this paper we show how to approximate the equiva- lent kernel of the widely-used squared exponential (or Gaussian) kernel and related kernels. This is easiest for uniform input densities, but we also discuss the generalization to the non-uniform case. We show further that the equivalent kernel can be used to understand the learning curves for Gaussian processes, and investigate how kernel smoothing using the equivalent kernel compares to full Gaussian process regression. 1 I