logL_GP_mod_common_hp

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.

internal

An implementation for the multi-task Gaussian processes with common
mean framework. Two main algorithms, called 'Magma' and 'MagmaClust',
are available to perform predictions for supervised learning problems, in
particular for time series or any functional/continuous data applications.
The corresponding articles has been respectively proposed by Arthur Leroy,
Pierre Latouche, Benjamin Guedj and Servane Gey (2022)
<doi:10.1007/s10994-022-06172-1>, and Arthur Leroy, Pierre Latouche,
Benjamin Guedj and Servane Gey (2023) <https://jmlr.org/papers/v24/20-1321.html>.
Theses approaches leverage the learning of cluster-specific mean processes,
which are common across similar tasks, to provide enhanced prediction
performances (even far from data) at a linear computational cost (in
the number of tasks). 'MagmaClust' is a generalisation of 'Magma'
where the tasks are simultaneously clustered into groups, each being
associated to a specific mean process. User-oriented functions in the
package are decomposed into training, prediction and plotting
functions. Some basic features (classic kernels, training, prediction) of
standard Gaussian processes are also implemented.

Arthur Leroy

MagmaClustR

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

Pierre Latouche

Pierre Pathé

Alexia Grenouillat

Hugo Lelievre

logL_GP_mod_common_hp function

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

Arguments

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

<dl>

<dt>hp</dt>
<dd>A tibble, data frame of hyper-parameters.</dd>


<dt>db</dt>
<dd>A tibble containing the values we want to compute the logL on.
Required columns: ID, Input, Output. Additional covariate columns are
allowed.</dd>


<dt>mean</dt>
<dd>A vector, specifying the mean of the GP at the reference inputs.</dd>


<dt>kern</dt>
<dd>A kernel function.</dd>


<dt>post_cov</dt>
<dd>A matrix, covariance parameter of the hyper-posterior.
Used to compute the correction term.</dd>


<dt>pen_diag</dt>
<dd>A jitter term that is added to the covariance matrix to avoid
numerical issues when inverting, in cases of nearly singular matrices.</dd>

</dl>

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

Description

Usage

Value

Arguments

Examples