gr_GP_mod_common_hp_k

Gradient of the penalised elbo for multiple mean GPs with common HPs

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

gr_GP_mod_common_hp_k function

<dl><dt>hp</dt>
<dd>A tibble, data frame or named vector containing hyper-parameters.</dd>
<dt>db</dt>
<dd>A tibble containing the values we want to compute the elbo on.
Required columns: Input, Output. Additional covariate columns are allowed.</dd>
<dt>mean</dt>
<dd>A list of the k means of the GPs at union of observed timestamps.</dd>
<dt>kern</dt>
<dd>A kernel function</dd>
<dt>post_cov</dt>
<dd>A list of the k posterior covariance of the mean GP (mu_k).
Used to compute correction term (cor_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

Gradient of the penalised elbo for multiple mean GPs with common HPs — gr_GP_mod_common_hp_k

<dl>

<dt>hp</dt>
<dd>A tibble, data frame or named vector containing hyper-parameters.</dd>


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


<dt>mean</dt>
<dd>A list of the k means of the GPs at union of observed timestamps.</dd>


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


<dt>post_cov</dt>
<dd>A list of the k posterior covariance of the mean GP (mu_k).
Used to compute correction term (cor_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>

gr_GP_mod_common_hp_k: Gradient of the penalised elbo for multiple mean GPs with common HPs

Description

Usage

Value

Arguments

Examples