eglearn {graphicalExtremes}

Learning extremal graph structure

Description

Following the methodology from Engelke et al. (2022), fits an extremal graph structure using the neighborhood selection approach (see Meinshausen and Bühlmann (2006)) or graphical lasso (see Friedman et al. (2008)).

Usage

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

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 Meinshausen and Bühlmann (2006), Friedman et al. (2008).

complete_Gamma

Whether you want to try fto complete Gamma matrix. Default is 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.

References

Engelke S, Lalancette M, Volgushev S (2022). “Learning extremal graphical structures in high dimensions.” doi:10.48550/ARXIV.2111.00840, Available from https://arxiv.org/abs/2111.00840., 2111.00840, https://arxiv.org/abs/2111.00840.

Friedman J, Hastie T, Tibshirani R (2008). “Sparse inverse covariance estimation with the graphical lasso.” Biostatistics, 9(3), 432–441.

Meinshausen N, Bühlmann P (2006). “High-dimensional graphs and variable selection with the Lasso.” Ann. Statist., 34(3), 1436 – 1462. doi:10.1214/009053606000000281.

See Also

Other structure estimation methods: data2mpareto(), eglatent(), emst(), fit_graph_to_Theta()

Examples

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