aagnesLambdaSelection: Augmented-MSE regularization parameter selection
In ldstatsHD: Linear Dependence Statistics for High-Dimensional Data

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

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

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)

`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 λ.
`many`	If `oneByone = TRUE`, the estimation process is done separately for every `many` λ's.

A-MSE algorithm finds λ by minimizing the risk function

R_{AMSE}(λ) = E(∑_{i>j} |δ_{ij}-\hat{δ}_{ij}^{λ}|^2)

where \hat{δ}_{ij}^{λ} is the dissimilarity matrix of the graph (see graphCorr). The expected value is approximated by either subsampling or Monte Carlo and the theoretical δ_{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.

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"`.

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

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.

lambdaSelection for other lambda selection approaches.

# 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)