e_step

Expectation step of the EM algorithm to compute the parameters of the
hyper-posterior Gaussian distribution of the mean process in Magma.

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

e_step function

<dl><dt>db</dt>
<dd>A tibble or data frame. Columns required: ID, Input, Output.
Additional columns for covariates can be specified.</dd>
<dt>m_0</dt>
<dd>A vector, corresponding to the prior mean of the mean GP.</dd>
<dt>kern_0</dt>
<dd>A kernel function, associated with the mean GP.</dd>
<dt>kern_i</dt>
<dd>A kernel function, associated with the individual GPs.</dd>
<dt>hp_0</dt>
<dd>A named vector, tibble or data frame of hyper-parameters
associated with <code>kern_0</code>.</dd>
<dt>hp_i</dt>
<dd>A tibble or data frame of hyper-parameters
associated with <code>kern_i</code>.</dd>
<dt>pen_diag</dt>
<dd>A number. A jitter term, added on the diagonal to prevent
numerical issues when inverting nearly singular matrices.</dd></dl>

Arguments

E-Step of the EM algorithm — e_step

<dl>

<dt>db</dt>
<dd>A tibble or data frame. Columns required: ID, Input, Output.
Additional columns for covariates can be specified.</dd>


<dt>m_0</dt>
<dd>A vector, corresponding to the prior mean of the mean GP.</dd>


<dt>kern_0</dt>
<dd>A kernel function, associated with the mean GP.</dd>


<dt>kern_i</dt>
<dd>A kernel function, associated with the individual GPs.</dd>


<dt>hp_0</dt>
<dd>A named vector, tibble or data frame of hyper-parameters
associated with <code>kern_0</code>.</dd>


<dt>hp_i</dt>
<dd>A tibble or data frame of hyper-parameters
associated with <code>kern_i</code>.</dd>


<dt>pen_diag</dt>
<dd>A number. A jitter term, added on the diagonal to prevent
numerical issues when inverting nearly singular matrices.</dd>

</dl>

e_step: E-Step of the EM algorithm

Description

Usage

Value

Arguments

Examples