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2004

Using the Equivalent Kernel to Understand Gaussian Process Regression

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Using the Equivalent Kernel to Understand Gaussian Process Regression
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 (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. Consider the supervised regression problem for a dataset D with entries (xi, yi) for i = 1, . . . , n. Under Gaussian Process (GP) assumptions the predictive mean at a test point x is given by
Peter Sollich, Christopher K. I. Williams
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where NIPS
Authors Peter Sollich, Christopher K. I. Williams
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