Gaussian process regression: a function space perspective
This page attempts an intuitive explanation of the function space perspective of Gaussian process (GP) regression. The webapp below demonstrates how a GP prior is a distribution over functions, and how observing data conditions the prior to obtain the GP posterior.
In the beginning there is just the Gaussian process (GP) prior, which is a vague specification of the function generating the data. You can see in the app below, samples from the GP prior (shown in orange) produce all sorts of random functions.
When a data-point is observed (click on the chart to add a data point), it conditions the values the GP can take at that point. Thus, observed data-points add information that constrains the distribution of functions. Vary the GP hyper-parameters to see how these affect the conditioning of the GP. When all the data has been observed, we are left with the posterior GP distribution over functions.
|Prior function covariance|
|Input noise precision|