extrapolation using Gaussian processes regression or Kriging

Question

Is there any way to estimate the extrapolation using kriging or Gaussian processes regression ?

Gaussian processes work very well for interpolation of scattered data; however, I need to extrapolate a time series of variable in time.

hoe can I extrapolate the x(n+1) using the history of x variable, x_i , i = n, n-1 ,....

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for example, in python: scikit-learn.org/stable/modules/gaussian_process.html

Answer 1

Extrapolation works in the same way theoretically and practically.

In theory, when you learn a Gaussian process regression model, you have modelled a Gaussian process on your data, you selected its mean function, its covariance function and have estimated their parameters. To interpolate (or extrapolate), you compute the mean of this Gaussian process at a new point, knowing the learning points.

In practice, for both interpolation and extrapolation, you just have to call a prediction function (called predict in R package DiceKriging and in scikit-learn in python).

However, you must known that Gaussian process regression (as many of the regression techniques [citation needed] works quite bad in extrapolation. The Gaussian process mean quickly "returns" to the function mean you have defined. Then, Gaussian process regression in extrapolation is just parametric regression whose model is the one you have chosen for the mean function.