Clustering and Prediction using Multi-Task Gaussian Processes with Common Mean
Compute the Multivariate Gaussian likelihood
Draw a number
Gradient of the penalised elbo for multiple mean GPs with common HPs
Mixture initialisation with kmeans
Create covariance matrix from a kernel
Create inverse of a covariance matrix from a kernel
Linear Kernel
Compute a covariance matrix for multiple individuals
Select the optimal number of clusters
Inverse a matrix using an adaptive jitter term
Allocate training data into the most probable cluster
Gradient of the elbo for a mixture of GPs
Round a matrix to make if symmetric
E-Step of the EM algorithm
Penalised elbo for multiple individual GPs with common HPs
Evidence Lower Bound for a mixture of GPs
Penalised elbo for multiple mean GPs with common HPs
Evidence Lower Bound maximised in MagmaClust
Expand a grid of inputs
Gradient of the penalised elbo for multiple individual GPs with common...
Gradient of the modified logLikelihood with common HPs for GPs in Magm...
Gradient of the modified logLikelihood for GPs in Magma
Gradient of the logLikelihood of a Gaussian Process
Gradient of the mixture of Gaussian likelihoods
Generate random hyper-parameters
Compute the hyper-posterior distribution for each cluster in MagmaClus...
Compute the hyper-posterior distribution in Magma
Run a k-means algorithm to initialise clusters' allocation
Compute an inverse covariance matrix for multiple individuals
Modified log-Likelihood function with common HPs for GPs
Modified log-Likelihood function for GPs
Log-Likelihood function of a Gaussian Process
Log-Likelihood for monitoring the EM algorithm in Magma
Squared Exponential Kernel
M-Step of the EM algorithm
MagmaClustR : Clustering and Prediction using Multi-Task Gaussian Proc...
Periodic Kernel
Pipe operator
Plot smoothed curves of raw data
Create a GIF of Magma or GP predictions
Plot Magma or GP predictions
Plot MagmaClust predictions
Display realisations from a (mixture of) GP prediction
Magma prediction for ploting GIFs
Gaussian Process prediction
Magma prediction
MagmaClust prediction
Indicates the most probable cluster
Regularise a grid of inputs in a dataset
Rational Quadratic Kernel
Draw samples from a posterior GP/Magma distribution
Draw samples from a MagmaClust posterior distribution
Simulate a dataset tailored for MagmaClustR
Simulate a batch of data
Compute a mixture of Gaussian log-likelihoods
Prediction in MagmaClust: learning new HPs and mixture probabilities
Learning hyper-parameters of a Gaussian Process
Training Magma with an EM algorithm
Training MagmaClust with a Variational EM algorithm
Update the mixture probabilities for each individual and each cluster
E-Step of the VEM algorithm
V-Step of the VEM algorithm
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.
Useful links