vm_step: V-Step of the VEM algorithm

In MagmaClustR: Clustering and Prediction using Multi-Task Gaussian Processes with Common Mean

V-Step of the VEM algorithm

Description

Maximization step of the Variational EM algorithm used to compute hyper-parameters of all the kernels involved in MagmaClust.

Usage

vm_step(
  db,
  old_hp_k,
  old_hp_i,
  list_mu_param,
  kern_k,
  kern_i,
  m_k,
  common_hp_k,
  common_hp_i,
  pen_diag
)

Arguments

db	A tibble or data frame. Columns required: ID, Input, Output. Additional columns for covariates can be specified.
old_hp_k	A named vector, tibble or data frame, containing the hyper-parameters from the previous M-step (or initialisation) associated with the mean GPs.
old_hp_i	A named vector, tibble or data frame, containing the hyper-parameters from the previous M-step (or initialisation) associated with the individual GPs.
list_mu_param	List of parameters of the K mean GPs.
kern_k	A kernel used to compute the covariance matrix of the mean GP at corresponding timestamps.
kern_i	A kernel used to compute the covariance matrix of individuals GP at corresponding timestamps.
m_k	A named list of prior mean parameters for the K mean GPs. Length = 1 or nrow(unique(db$Input))
common_hp_k	A boolean indicating whether hp are common among mean GPs (for each mu_k)
common_hp_i	A boolean indicating whether hp are common among individual GPs (for each y_i)
pen_diag	A number. A jitter term, added on the diagonal to prevent numerical issues when inverting nearly singular matrices.

Value

A named list, containing the elements hp_k, a tibble containing the hyper-parameters associated with each cluster, hp_i, a tibble containing the hyper-parameters associated with the individual GPs, and prop_mixture_k, a tibble containing the hyper-parameters associated with each individual, indicating the probabilities to belong to each cluster.

Examples

TRUE

MagmaClustR documentation built on June 29, 2024, 1:06 a.m.