vulnLambdaSelection: Vulnerability regularization parameter selection
In ldstatsHD: Linear Dependence Statistics for High-Dimensional Data

Description Usage Arguments Details Value Author(s) References See Also Examples

vulLambdaSelection is a function designed to select the regularization parameter in graphical models. It selects the graph with largest average nodes vulnerability.

1	vulLambdaSelection(obj, loo = FALSE, subOut = 10, nite = 50)

`obj`	an object of class `huge`, `camel.tiger` or `wfgl`.
`loo`	if `TRUE` an exhaustive leave-one-out procedure is done, otherwise it is used a subsampling approach with `nite` iterations and leaving out `subOut` variables.
`subOut`	number of variables left out in each iteration (only used if `loo = FALSE`).
`nite`	number of iterations (only used if `loo = FALSE`).

Vulnerability algorithm finds lambda by minimizing the risk function

R_{VUL}(λ) = - ∑_{i=1}^p \frac{E^λ-E_i^λ}{E^λ}

where E^λ is the global efficiency of the original network and E^λ_i is the global efficiency of the network once eliminating the node i. Global efficiency is defined by the harmonic mean of the geodesic distance (see graphDist).

Vulnerability gives λ selection that contains the most vulnerable graph, meaning that the removal of a node in the network in average would affect the most the estimated graph.

An object of class lambdaSelection containing the following components:

`opt.lambda`	optimal lambda.
`crit.coef`	coefficients for each lambda given the criterion VUL.
`criterion`	with value `"VUL"`.

Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.

Costa, L. and F. Rodrigues (2007). Characterization of complex networks: A survey of measurements. Advances in Physics 56(1), 167-242.

lambdaSelection for other lambda selection approaches.

# example to use vul function
EX1         <- pcorSimulator(nobs = 50, nclusters = 2, nnodesxcluster = c(40,30), 
                             pattern="powerLaw")
y           <- EX1$y
Lambda.SEQ  <- seq(.35, 0.70, length.out = 10)
out3        <- huge(y, method = "mb", lambda = Lambda.SEQ)
## not run
#VUL.COEF    <- vulLambdaSelection(out3)
#print(VUL.COEF)