# selectFast: Estimate a graph in a Gaussian Graphical Model: Fast... In GGMselect: Gaussian Graphs Models Selection

## Description

Select a graph within the (data-driven) families of graphs `EW`, `C01`, and `LA`.

## Usage

 ```1 2 3 4 5``` ```selectFast(X, dmax=min(floor(nrow(X)/3),nrow(X)-3,ncol(X)-1), K=2.5, family="EW", min.ev=10**(-8), max.iter=200, eps=0.01, beta=nrow(X)*nrow(X)/2, tau=1/sqrt(nrow(X)*(ncol(X)-1)), h=0.001, T0=10, verbose=FALSE ) ```

## Arguments

 `X` `n x p` matrix where `n` is the sample size and `p` the number of variables. `n` should be greater than `3` and `p` greater than `1`. `dmax` integer or `p`-dimensional vector of integers smaller or equal to `min(n-3, p-1)`. When `dmax` is a scalar, it gives the maximum degree of the estimated graph. When `dmax` is a vector, `dmax[a]` gives the maximum degree of the node `a`. `K` scalar or vector with values greater than 1. Tuning parameter of the penalty function. `family` character string or vector of character strings, among `"EW"`, `"LA"`, `"C01"`, `c("C01","LA")` or `c("C01","LA","EW")`. `min.ev` minimum eigenvalue for matrix inversion. `max.iter, eps, beta, tau, h, T0` tuning parameters for the Langevin Monte Carlo algorithm. Only used when `family` is `"EW"` or `c("C01","LA","EW")`. `verbose` logical. If `TRUE` a trace of the current process is displayed in real time.

## Details

More details are available on ../doc/Notice.pdf

## Value

A list with components `"EW"`, `"LA"`, `"C01"`, `"C01.LA"` and `"C01.LA.EW"`, according to the `family` argument, each one with components:

 `Neighb ` array of dimension ```p x max(dmax) x length(K)``` or, when `length(K)` equals 1, matrix of dimension `p x max(dmax)`. `Neighb[a, , k ]` contains the indices of the nodes connected to node `a` for `K[k]`. `crit.min` vector of dimension `length(K)`. It gives the minimal values of the selection criterion for each value of `K` `G` array of dimension `p x p x length(K)` or, when `length(K)` equals 1, matrix of dimension `p x p`. `G[,,k]` gives the adjacency matrix for `K[k]`.

## Author(s)

Bouvier A, Giraud C, Huet S, Verzelen N.

## References

Please use `citation("GGMselect")`.

## See Also

`selectQE`, `selectMyFam`, `simulateGraph`, `penalty`, `convertGraph`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```p=30 n=30 # simulate graph eta=0.11 Gr <- simulateGraph(p,eta) # simulate data X <- rmvnorm(n, mean=rep(0,p), sigma=Gr\$C) # estimate graph GRest <- selectFast(X, family="C01") # plot result library(network) par(mfrow=c(1,2)) gV <- network(Gr\$G) plot(gV,jitter=TRUE, usearrows = FALSE, label=1:p,displaylabels=TRUE) g <- network(GRest\$C01\$G) plot(g, jitter=TRUE, usearrows = FALSE, label=1:p,displaylabels=TRUE) ```

GGMselect documentation built on Jan. 10, 2020, 9:07 a.m.