Bagged Cort copulas

Source: R/CortForest.R

CortForest class

CortForest(
  x,
  p_value_for_dim_red = 0.75,
  n_trees = 10,
  compte_loo_weights = FALSE,
  min_node_size = 1,
  pseudo_data = FALSE,
  number_max_dim = NULL,
  verbose_lvl = 2,
  force_grid = FALSE,
  oob_weighting = TRUE
)

Arguments

x

The data, must be provided as a matrix with each row as an observation.

p_value_for_dim_red

a p_value for the localised dimension reduction test

n_trees

Number of trees

compte_loo_weights

Defaults to FALSE. Allows to use an automatic re-weighting of the trees in the forest, based on leave-one-out considerations.

min_node_size

The minimum number of observation avaliable in a leaf to initialise a split.

pseudo_data

set to True if you are already providing data on the copula space.

number_max_dim

The maximum number of dimension a split occurs in. Defaults to be all of the dimensions.

verbose_lvl

verbosity level : can be 0 (default) or an integer. bigger the integer bigger the output level.

force_grid

boolean (default: FALSE). set to TRUE to force breakpoint to be on the n-checkerboard grid in every tree.

oob_weighting

boolean (default : TRUE) option to weight the trees with an oob criterion (otherwise they are equally weighted)

Value

An instance of the CortForest S4 class. The object represent the fitted copula and can be used through several methods to query classical (r/d/p/v)Copula methods, constraint influence, etc. Beside returning some inputted parameters, notable slots are :

  • trees A list of Cort objects representing each fitted tree in the forest.

  • weights The weigths of each tree.

  • indexes The indexes of data points that were selected for fitting the trees

  • pmf The density of each tree on data points

  • norm_matrix The matrix of scalar product between trees

  • oob_pmf The density of each tree on data points it did not see during fitting

  • oob_kl The out-of-bag Kullback-Leibler divergence of each tree

  • oob_ise The out-of-bag Integrated Square Error of each tree

More details about these slots can be found in the reference.

Details

This class implements the bagging of CORT models, with an out-of-bag error minimisation in the weights.

See O. Laverny, V. Maume-Deschamps, E. Masiello and D. Rullière (2020) for the details of this density estimation procedure, and vignettes(package='cort') for examples of usecases.

References

laverny2020cort

Examples

(CortForest(LifeCycleSavings[,1:3],number_max_dim=2,n_trees=2))
#> ======================== Computing trees...
#> ======================== Computing statistics...
#>      Computing pmf...
#>      Computing norm matrix...
#>      Computing weights...
#> 
#> Call:
#> nloptr(x0 = x0, eval_f = fn, eval_grad_f = gr, lb = lower, ub = upper, 
#>     eval_g_ineq = hin, eval_jac_g_ineq = hinjac, eval_g_eq = heq, 
#>     eval_jac_g_eq = heqjac, opts = opts)
#> 
#> 
#> Minimization using NLopt version 2.7.1 
#> 
#> NLopt solver status: 3 ( NLOPT_FTOL_REACHED: Optimization stopped because 
#> ftol_rel or ftol_abs (above) was reached. )
#> 
#> Number of Iterations....: 5 
#> Termination conditions:  stopval: -Inf	xtol_rel: 1e-10	maxeval: 1e+06	ftol_rel: 1e-10	ftol_abs: 1e-10 
#> Number of inequality constraints:  0 
#> Number of equality constraints:    1 
#> Optimal value of objective function:  0.24957689853439 
#> Optimal value of controls: 0.6979554 0.3020446
#> 
#> 
#>      Computing oob stats...
#> ======================== Done !
#> CortForest copula model: 50x3-dataset and 2 Cort trees.