eglearn: Learning extremal graph structure

Description

Following the methodology from eng2022a;textualgraphicalExtremes, fits an extremal graph structure using the neighborhood selection approach (see meins2006;textualgraphicalExtremes) or graphical lasso (see friedman2008;textualgraphicalExtremes).

Usage

eglearn(
  data,
  p = NULL,
  rholist = c(0.1, 0.15, 0.19, 0.205),
  reg_method = c("ns", "glasso"),
  complete_Gamma = FALSE
)

Value

List made of:

graph: A list of igraph::graph objects representing the fitted graphs for each rho in rholist.
Gamma: A list of numeric estimated \(d \times d\) variogram matrices \(\Gamma\) corresponding to the fitted graphs, for each rho in rholist. If complete_Gamma = FALSE or the underlying graph is not connected, it returns NULL.
rholist: The list of penalty coefficients.
graph_ic: A list of igraph::graph objects representing the optimal graph according to the aic, bic, and mbic information criteria. If reg_method = "glasso", it returns a list of NULL.
Gamma_ic: A list of numeric \(d \times d\) estimated variogram matrices \(\Gamma\) corresponding to the aic, bic, and mbic information criteria. If reg_method = "glasso", complete_Gamma = FALSE, or the underlying graph is not connected, it returns a list of NULL.

Arguments

data: Numeric \(n \times d\) matrix, where n is the number of observations and d is the dimension.
p: Numeric between 0 and 1 or NULL. If NULL (default), it is assumed that the data are already on multivariate Pareto scale. Else, p is used as the probability in the function data2mpareto() to standardize the data.
rholist: Numeric vector of non-negative regularization parameters for the lasso. Default is rholist = c(0.1, 0.15, 0.19, 0.205). For details see glasso::glassopath().
reg_method: One of "ns", "glasso", for neighborhood selection and graphical lasso, respectively. Default is reg_method = "ns". For details see meins2006;textualgraphicalExtremes, friedman2008;textualgraphicalExtremes.
complete_Gamma: Whether you want to try fto complete Gamma matrix. Default is complete_Gamma = FALSE.

References

Examples

Run this code

set.seed(2)
m <- generate_random_model(d=6)
y <- rmpareto(n=500, par=m$Gamma)
ret <- eglearn(y)