ldstatsHD (version 1.0.1)

amseLambdaSelection: Augmented-MSE regularization parameter selection

Description

amseLambdaSelection is a function designed to select the regularization parameter lambda in graphical models that compromises global clustering structure and variability of the graph.

Usage

amseLambdaSelection(obj, pathIni, y, generator = c("subsampling", "montecarlo"),
                    pB = 0.7, nite = 10, method = "mb", from = 1, until = NULL, 
                    distF = c("correlation","shortPath"), oneByone = FALSE, 
                    many = 3)

Arguments

obj

an object of class huge or camel.tiger.

pathIni

path with best global characteristics (for instance the agnesLambdaSelection selected path).

y

original \(n\times p\) data set.

generator

type of generator to find the mean squared error: name that uniquely identifies "subsampling" or "montecarlo".

pB

proportion of observations used in subsampling iterations.

nite

number of iterations used to estimate the mean square error.

method

method used to estimate the networks: name that uniquely identifies "mb", "glasso" or "tiger".

from

starting point in lambda sequence.

until

last point in lambda sequence. If until = NULL, all lambda sequence is explored.

distF

distance function used to find the dissimilarity matrix from the graph: name that uniquely identifies "correlation" or "shortPath".

oneByone

If TRUE, the estimation process is done separately for each \(\lambda\).

many

If oneByone = TRUE, the estimation process is done separately for every many \(\lambda\)'s.

Value

An object of class lambdaSelection containing the following components:

opt.lambda

optimal lambda.

crit.coef

coefficients for each lambda given the criterion A-MSE.

criterion

with value "A-MSE".

Details

A-MSE algorithm finds \(\lambda\) by minimizing the risk function $$ R_{AMSE}(\lambda) = E(\sum_{i>j} |\delta_{ij}-\hat{\delta}_{ij}^{\lambda}|^2) $$ where \(\hat{\delta}_{ij}^{\lambda}\) is the dissimilarity matrix of the graph (see graphCorr). The expected value is approximated by either subsampling or Monte Carlo and the theoretical \(\delta_{ij}\) is approximated by the graph in pathIni.

We recommend using the AGNES algorithm agnesLambdaSelection to approximate pathIni since provides good reference of global network structure for clustered-based graph structures. Then, A-MSE gives a good trade-off between graph variability and global network characteristics.

If pathIni is given by agnesLambdaSelection and generator = "subsampling", then the lambda selected is always smaller than the lambda obtained by AGNES.

The oneByone approach is suggested to save memory space for very high-dimensional data.

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.

See Also

lambdaSelection for other lambda selection approaches.

Examples

# NOT RUN {
# example to use amse function
EX1         <- pcorSimulator(nobs = 70, nclusters = 3, nnodesxcluster = c(40,30,20), 
                             pattern = "powerLaw")
y           <- EX1$y
Lambda.SEQ  <- seq(.25, 0.70, length.out = 40)
out3        <- huge(y, method = "mb", lambda = Lambda.SEQ)
AG.COEF     <- agnesLambdaSelection(out3, distF = "shortPath", way = "direct")
AG.LAMB     <- which(AG.COEF$opt.lambda == Lambda.SEQ)

## not run
#AAG.COEF    <- amseLambdaSelection(out3, out3$path[[AG.LAMB]], y = y, 
#                 distF = "shortPath", from = AG.LAMB)
#print(AAG.COEF) 

# }