Understanding Gaussian Process Regression Using the Equivalent Kernel
Peter Sollich and Christopher Williams
Lecture notes in computer science
The equivalent kernel is a way of understanding
how Gaussian process regression works for large sample sizes based on
a continuum limit. In this
paper we show how to approximate the equivalent 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.