# Specifying mean and kernel function in Gaussian Process

As part of the Improved Machine Learning in Mathematica 11, Wolfram advertises the Method "GaussianProcess" which can be used with Predict[] to obtain smooth Gaussian random fields. The screenshot below from the official documentation shows how this is applied.

However, I was wondering if I can somehow specify the mean function $\boldsymbol{\mu}$ and covariance kernel function $k(x_i, x_j)$? I cannot find it in the documentation of Predict[], or anywhere else in the Wolfram documentation. Perhaps there is an undocumented option to provide the mean and kernel function?

I am referring $\mu$ and $k$ as used in this paper this paper.

As far as I know, it's not yet possible to specify arbitrary covariance kernels. However, there are a few ways to control the kernel type. You can specify the type of covariance function using the "CovarianceType" suboption like so:

pred = Predict[data,
Method -> {
"GaussianProcess",
"CovarianceType" -> "Linear"
}
]


The possible kernels for "CovarianceType" are:

{
"Periodic", "SquaredExponential", "RationalQuadratic", "Linear",
"Mattern5/2", "Mattern3/2", "NN", "WN"
}


You can also specify algebraic combinations of these kernels, such as:

"CovarianceType" -> "Linear" + "Periodic" * "RationalQuadratic"


Finally, there is the "Composite" option value, which will try and find a sensible combination of kernels that works well. Furthermore, there is the "SearchMethod" suboption for composite kernels, which can be set to "Greedy" or "SimulatedAnnealing". E.g.:

Method -> {
"GaussianProcess",
"CovarianceType" -> "Composite",
"SearchMethod" -> "SimulatedAnnealing"
}


After the predictor pred has been computed, you can investigate what it's using by evaluating:

pred[[1]]


# Edit

As far as I know, there is currently no implementation of mean functions, but I might be wrong about that.

# Edit 2

Since I answered this question, the documentation has been updated. Be sure to check it for any updates to the GaussianProcess method:

http://reference.wolfram.com/language/ref/method/GaussianProcess.html