Applications
A Gaussian process can be used as a prior probability distribution over functions in Bayesian inference. Given any set of points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of your N points with some desired kernel, and sample from that Gaussian.
Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, or kriging; extending Gaussian process regression to multiple target variables is known as co-kriging. As such, Gaussian processes are useful as a powerful non-linear interpolation tool. Additionally, Gaussian process regression can be extend to address learning tasks both in a supervised (e.g. probabilistic classification) and an unsupervised (e.g. manifold learning) learning framework.
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