update_mixture

Update the mixture probabilities for each individual and each cluster

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

update_mixture function

<dl><dt>db</dt>
<dd>A tibble or data frame. Columns required: <code>ID</code>,
<code>Input</code>, <code>Output</code>. Additional columns for covariates can be
specified.</dd>
<dt>mean_k</dt>
<dd>A list of the K hyper-posterior mean parameters.</dd>
<dt>cov_k</dt>
<dd>A list of the K hyper-posterior covariance matrices.</dd>
<dt>hp</dt>
<dd>A named vector, tibble or data frame of hyper-parameters
associated with <code>kern</code>, the individual process' kernel. The
columns/elements should be named according to the hyper-parameters
that are used in <code>kern</code>.</dd>
<dt>kern</dt>
<dd>A kernel function, defining the covariance structure of
the individual GPs.</dd>
<dt>prop_mixture</dt>
<dd>A tibble containing the hyper-parameters associated
with each individual, indicating in which cluster it belongs.</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

Update the mixture probabilities for each individual and each cluster — update_mixture

<dl>

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


<dt>mean_k</dt>
<dd>A list of the K hyper-posterior mean parameters.</dd>


<dt>cov_k</dt>
<dd>A list of the K hyper-posterior covariance matrices.</dd>


<dt>hp</dt>
<dd>A named vector, tibble or data frame of hyper-parameters
associated with <code>kern</code>, the individual process' kernel. The
columns/elements should be named according to the hyper-parameters
that are used in <code>kern</code>.</dd>


<dt>kern</dt>
<dd>A kernel function, defining the covariance structure of
the individual GPs.</dd>


<dt>prop_mixture</dt>
<dd>A tibble containing the hyper-parameters associated
with each individual, indicating in which cluster it belongs.</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>

update_mixture: Update the mixture probabilities for each individual and each cluster

Description

Usage

Value

Arguments

Examples