Abstract
The equivalent kernel [1] 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.
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Sollich, P., Williams, C.K.I. (2005). Understanding Gaussian Process Regression Using the Equivalent Kernel. In: Winkler, J., Niranjan, M., Lawrence, N. (eds) Deterministic and Statistical Methods in Machine Learning. DSMML 2004. Lecture Notes in Computer Science(), vol 3635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11559887_13
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DOI: https://doi.org/10.1007/11559887_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29073-5
Online ISBN: 978-3-540-31728-9
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