# agnesLambdaSelection: AGNES regularization parameter selection In ldstatsHD: Linear Dependence Statistics for High-Dimensional Data

## Description

agnesLambdaSelection is a function designed to select the regularization parameter in graphical models. It selects the most clustered conditional dependence graph structure where clusters are defined by the hierarchical algorithm agnes (See details).

## Usage

 1 2 3 4 agnesLambdaSelection(obj, way = "direct", nite = 10, subsvec = NULL, eps = 0.05, until = NULL, minNodes = 30, distF = c("correlation","shortPath"))

## Arguments

 obj an object of class huge, camel.tiger or wfgl. way name that uniquely identifies "direct" (default), "rand.sampling" for random subsets algorithm and "int.sampling" for intelligent subsets algorithm. nite vector with the number of iterations used for each lambda (only if way = "rand.sampling" or way = "int.sampling"). subsvec vector with the number of subsamples used for each lambda (only if way = "rand.sampling" or way = "int.sampling"). If NULL, argument minNodes determines the number of subsamples for all lambdas. eps acceptance tolerance for subsets of variables. until the last path used in obj. If NULL, all paths are used to select lambda. minNodes minimum number of nodes with connections to compute the AGNES coefficient (the coefficient is zero for paths with less nodes than minNodes). distF distance function used to find the dissimilarity matrix from the graph: name that uniquely identifies "correlation" and "shortPath".

## Details

AGNES algorithm finds λ by minimizing the risk function

R_{AGNES}(λ) = -AC(λ)

where AC(λ) is the AGNES coefficient calculated using the R function agnes. Using AGNES we select the λ that maximizes the between vs within cluster dissimilarities ratio given the dissimilarity matrix of the graph (see graphCorr and graphDist for possible dissimilarities).

A variable subset selection algorithm is available to estimate AC(λ) for very high-dimensional data. It is recommended in order to save memory space and computational time. Especially way = "int.sampling" which tends to finds similar lambda selections to the default procedure.

agnesLambdaSelection gives a good recovery of global network characteristics when the true partial correlation matrix is block diagonal.

## Value

An object of class lambdaSelection containing the following components:

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

## Author(s)

Caballe, Adria <[email protected]>, Natalia Bochkina and Claus Mayer.

## References

Caballe, A., N. Bochkina, and C. Mayer (2016). Selection of the Regularization Parameter in Graphical Models using network charactaristics. eprint arXiv:1509.05326, 1-25.