kern_to_inv: Create inverse of a covariance matrix from a kernel

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

Create inverse of a covariance matrix from a kernel

Description

kern_to_inv() creates the inverse of 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_inv(input, kern, hp, pen_diag = 1e-10, deriv = 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.
pen_diag	A jitter term that is added to the covariance matrix to avoid numerical issues when inverting, in cases of nearly singular matrices.
deriv	A character, indicating according to which hyper-parameter the derivative should be computed. If NULL (default), the function simply returns the inverse covariance matrix.

Value

The inverse of a covariance matrix, which 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.