JGL {JGL}

Joint Graphical Lasso

Description

Solve the Joint Graphical Lasso

Usage

JGL(Y,penalty="fused",lambda1,lambda2,rho=1,weights="equal",penalize.diagonal=FALSE,
maxiter=500,tol=1e-5,warm=NULL,return.whole.theta=FALSE, screening="fast",
truncate = 1e-5)

Arguments

Y

A list of nXp data matrices.

penalty

Determines whether lambda2 controls a "fused" or "group" lasso penalty. Must take value "fused" or "group".

lambda1

The tuning parameter for the graphical lasso penalty.

lambda2

The tuning parameter for the fused or group lasso penalty.

rho

A step size parameter. Large values decrease step size.

weights

Determines the putative sample size of each class's data. Allowed values: a vector with length equal to the number of classes; "equal", giving each class weight 1; "sample.size", giving each class weight corresponding to its sample size.

penalize.diagonal

If penalty=="fused", determines whether lambda1 is applied to the diagonal of theta. If penalty=="group", determines whether lambda1 and lambda2 are applied to the diagonal of theta.

maxiter

Maximum number of iterations.

tol

Determines convergence criterion.

warm

Input a warm start to theta in the form of a K-length list of pXp matrices.

return.whole.theta

If TRUE, each class's inverse covariance matrix is returned whole. If FALSE, the inverse covariance matrix is only returned over the connected nodes, and only the diagonal of the matrix is returned over the unconnected nodes.

screening

"fast" or "memory.efficient". Use of "fast" is recommended unless the number of features prohibits storage of a pXp matrix. For very high dimension data, screening="memory.efficient" will allow a solution with a much longer computation time.

truncate

Defaults to 1e-5. At convergence, all values of theta below this number will be set to zero.

Details

This function can solve both the Fused Graphical Lasso and the Group Graphical Lasso.

Value

theta

A list of the estimated inverse covariance matrices, over all nodes if return.whole.theta==TRUE and over only the connected nodes if return.whole.theta==FALSE

diag.theta.unconnected

Returned only if return.whole.theta==FALSE. A list of vectors, each vector the estimated diagonal of an inverse covariance matrix over the unconnected nodes.

connected

A logical vector identifying whether each node is connected.

Author(s)

Patrick Danaher

References

Patrick Danaher, Pei Wang and Daniela Witten (2011). The joint graphical lasso for inverse covariance estimation across multiple classes. http://arxiv.org/abs/1111.0324

Examples

## load an example dataset with K=two classes, p=200 features, and n=100 samples per class:
data(example.data)
str(example.data)
## run fgl:
fgl.results = JGL(Y=example.data,penalty="fused",lambda1=.25,lambda2=.1)
str(fgl.results)
print.jgl(fgl.results)
## run ggl:
ggl.results = JGL(Y=example.data,penalty="group",lambda1=.15,lambda2=.2,return.whole.theta=TRUE)
str(ggl.results)
print.jgl(ggl.results)