kern_to_cov: Create covariance matrix from a kernel

In MagmaClustR: Clustering and Prediction using Multi-Task Gaussian Processes with Common Mean

Create covariance matrix from a kernel

Description

kern_to_cov() creates a covariance matrix between input values (that could be either scalars or vectors) evaluated within a kernel function, which is characterised by specified hyper-parameters. This matrix is a finite-dimensional evaluation of the infinite-dimensional covariance structure of a GP, defined thanks to this kernel.

Usage

kern_to_cov(input, kern = "SE", hp, deriv = NULL, input_2 = NULL)

Arguments

input	A vector, matrix, data frame or tibble containing all inputs for one individual. If a vector, the elements are used as reference, otherwise , one column should be named 'Input' to indicate that it represents the reference (e.g. 'Input' would contain the timestamps in time-series applications). The other columns are considered as being covariates. If no column is named 'Input', the first one is used by default.
kern	A kernel function. Several popular kernels (see The Kernel Cookbook) are already implemented and can be selected within the following list: "SE": (default value) the Squared Exponential Kernel (also called Radial Basis Function or Gaussian kernel), "LIN": the Linear kernel, "PERIO": the Periodic kernel, "RQ": the Rational Quadratic kernel. Compound kernels can be created as sums or products of the above kernels. For combining kernels, simply provide a formula as a character string where elements are separated by whitespaces (e.g. "SE + PERIO"). As the elements are treated sequentially from the left to the right, the product operator '*' shall always be used before the '+' operators (e.g. 'SE * LIN + RQ' is valid whereas 'RQ + SE * LIN' is not).
hp	A list, data frame or tibble containing the hyper-parameters used in the kernel. The name of the elements (or columns) should correspond exactly to those used in the kernel definition. If hp contains an element or a column 'Noise', its value will be added on the diagonal of the covariance matrix.
deriv	A character, indicating according to which hyper-parameter the derivative should be computed. If NULL (default), the function simply returns the covariance matrix.
input_2	(optional) A vector, matrix, data frame or tibble under the same format as input. This argument should be used only when the kernel needs to be evaluated between two different sets of inputs, typically resulting in a non-square matrix.

Value

A covariance matrix, where elements are evaluations of the associated kernel for each pair of reference inputs.

Examples

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MagmaClustR documentation built on June 29, 2024, 1:06 a.m.