rq_kernel

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

rq_kernel function

<dl><dt>x</dt>
<dd>A vector (or matrix if vectorized = T) of inputs.</dd>
<dt>y</dt>
<dd>A vector (or matrix if vectorized = T) of inputs.</dd>
<dt>hp</dt>
<dd>A tibble, data frame or named vector, containing the kernel's
hyperparameters. Required columns: 'rq_variance', 'rq_lengthscale', and
'rq_scale'.</dd>
<dt>deriv</dt>
<dd>A character, indicating according to which hyper-parameter the
derivative should be computed. If NULL (default), the function simply returns
the evaluation of the kernel.</dd>
<dt>vectorized</dt>
<dd>A logical value, indicating whether the function provides
a vectorized version for speeded-up calculations. If TRUE, the <code>x</code>
and <code>y</code> arguments should be the vector or matrix containing all
inputs for which the kernel is evaluated on all pairs of elements.
If FALSE, the <code>x</code> and <code>y</code> arguments are simply two inputs.</dd></dl>

Arguments

Rational Quadratic Kernel — rq_kernel

<dl>

<dt>x</dt>
<dd>A vector (or matrix if vectorized = T) of inputs.</dd>


<dt>y</dt>
<dd>A vector (or matrix if vectorized = T) of inputs.</dd>


<dt>hp</dt>
<dd>A tibble, data frame or named vector, containing the kernel's
hyperparameters. Required columns: 'rq_variance', 'rq_lengthscale', and
'rq_scale'.</dd>


<dt>deriv</dt>
<dd>A character, indicating according to which hyper-parameter the
derivative should be computed. If NULL (default), the function simply returns
the evaluation of the kernel.</dd>


<dt>vectorized</dt>
<dd>A logical value, indicating whether the function provides
a vectorized version for speeded-up calculations. If TRUE, the <code>x</code>
and <code>y</code> arguments should be the vector or matrix containing all
inputs for which the kernel is evaluated on all pairs of elements.
If FALSE, the <code>x</code> and <code>y</code> arguments are simply two inputs.</dd>

</dl>

Rational Quadratic Kernel

rq_kernel: Rational Quadratic Kernel

Description

Usage

Value

Arguments

Examples