Prediction in MagmaClust: learning new HPs and mixture probabilitiesSource:
Learning hyper-parameters and mixture probabilities of any new
individual/task is required in
MagmaClust in the prediction procedure.
By providing data for the new individual/task, the hyper-posterior mean and
covariance parameters, the mixture proportions, and initialisation values for
train_gp_clust uses an EM algorithm to compute
maximum likelihood estimates of the hyper-parameters and hyper-posterior
mixture probabilities of the new individual/task.
train_gp_clust( data, prop_mixture = NULL, ini_hp = NULL, kern = "SE", hyperpost = NULL, pen_diag = 1e-10, n_iter_max = 25, cv_threshold = 0.001 )
A tibble or data frame. Required columns:
Output. Additional columns for covariates can be specified. The
Inputcolumn should define the variable that is used as reference for the observations (e.g. time for longitudinal data). The
Outputcolumn specifies the observed values (the response variable). The data frame can also provide as many covariates as desired, with no constraints on the column names. These covariates are additional inputs (explanatory variables) of the models that are also observed at each reference
A tibble or a named vector. Each name of column or element should refer to a cluster. The value associated with each cluster is a number between 0 and 1, corresponding to the mixture proportions.
A tibble or data frame of hyper-parameters associated with
kern, the individual process kernel.
A kernel function, defining the covariance structure of the GP. Several popular kernels (see The Kernel Cookbook) are already implemented and can be selected within the following list:
"SE": (default value) the Squared Exponential Kernel (also called Radial Basis Function or Gaussian kernel),
"LIN": the Linear kernel,
"PERIO": the Periodic kernel,
"RQ": the Rational Quadratic kernel. Compound kernels can be created as sums or products of the above kernels. For combining kernels, simply provide a formula as a character string where elements are separated by whitespaces (e.g. "SE + PERIO"). As the² elements are treated sequentially from the left to the right, the product operator '*' shall always be used before the '+' operators (e.g. 'SE * LIN + RQ' is valid whereas 'RQ + SE * LIN' is not).
A list, containing the elements
mixturethe parameters of the hyper-posterior distributions of the mean processes. Typically, this argument should come from a previous learning using
train_magmaclust, or a previous prediction with
pred_magmaclust, with the argument
get_hyperpostset to TRUE.
A number. A jitter term, added on the diagonal to prevent numerical issues when inverting nearly singular matrices.
A number, indicating the maximum number of iterations of the EM algorithm to proceed while not reaching convergence.
A number, indicating the threshold of the likelihood gain under which the EM algorithm will stop.
A list, containing the results of the EM algorithm used during the prediction step of MagmaClust. The elements of the list are:
hp: A tibble of optimal hyper-parameters for the new individual's GP.
mixture: A tibble of mixture probabilities for the new individual.