logL_GP_mod_common_hp: Modified log-Likelihood function with common HPs for GPs

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

Modified log-Likelihood function with common HPs for GPs

Description

Log-Likelihood function involved in Magma during the maximisation step of the training, in the particular case where the hyper-parameters are shared by all individuals. The log-Likelihood is defined as a sum over all individuals of Gaussian likelihoods added with correction trace terms.

Usage

logL_GP_mod_common_hp(hp, db, mean, kern, post_cov, pen_diag)

Arguments

hp	A tibble, data frame of hyper-parameters.
db	A tibble containing the values we want to compute the logL on. Required columns: ID, Input, Output. Additional covariate columns are allowed.
mean	A vector, specifying the mean of the GP at the reference inputs.
kern	A kernel function.
post_cov	A matrix, covariance parameter of the hyper-posterior. Used to compute the correction term.
pen_diag	A jitter term that is added to the covariance matrix to avoid numerical issues when inverting, in cases of nearly singular matrices.

Value

A number, corresponding to the value of the modified Gaussian log-Likelihood with common hyper-parameters defined in Magma.

Examples

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