dpglasso: dpglasso
In dpglasso: Primal Graphical Lasso

Description Usage Arguments Details Value Author(s) References Examples

View source: R/dpglasso.R

Does block (one row/column at a time) coordinate-wise optimization on the primal of the Graphical Lasso problem:

min_X log det (X) + trace(X Sigma) + rho |X|_1

1	dpglasso(Sigma, X=NULL,invX=NULL,rho,outer.Maxiter=100,obj.seq=FALSE,outer.tol=10^-5)

`Sigma`	(Required) the sample covariance matrix, symmetric PSD with dimensions p \times p.
`X`	is an initialization to the precision matrix X. It must be symmetric, PD with dimensions p \times p. Defaults to `X= diag( 1/(rep(rho,p) + diag(Sigma)) )`
`invX`	is an initialization to the covariance matrix. It must be symmetric with dimensions p \times p. It is not necessary for `invX` to be the inverse of `X`. Defaults to `invX<- Sigma + diag(rep(rho,p))`
`rho`	(Required) is the amount of regularization. It is a non-negative scalar.
`outer.Maxiter`	the maximum number of outer iterations (i.e. row/column updates) to be performed. `outer.Maxiter` defaults to 100.
`obj.seq`	Logical variable taking values `TRUE/FALSE`. If `obj.seq=TRUE` dpglasso computes the objective value after every sweep across p rows/columns. `obj.seq` defaults to `FALSE` Note: Computing the objective values is O(p^3), and can take quite some time depending upon the size of the problem. Hence, it is not recommended to compute the objective values, during the course of the algorithm.
`outer.tol`	convergence criterion. `outer.tol` is a non-negative scalar. If relative difference in the frobenius norm of the precision matrices across two successive iterations is below `outer.tol`, algorithm `dpglasso` converges.

dpglasso can also be used as a path algorithm ie solve problem (A) on a grid of rho values. In that case, the estimates of the precision matrix X and covariance matrix invX obtained by solving (A) for a certain rho, are to be supplied as warm-starts to solve problem (A) for a smaller value of rho. See the example below.

`X`	precision matrix
`invX`	covariance matrix
`time.counter.QP`	This is a three dimensional vector, representing the total time taken to solve all the QPs; uses the R function `proc.time()`

Rahul Mazumder and Trevor Hastie

This algorithm DPGLASSO is described in the paper: “The Graphical Lasso: New Insights and Alternatives by Rahul Mazumder and Trevor Hastie" available at http://arxiv.org/abs/1111.5479

set.seed(2008)

# create data

n=10; p = 5; 
X<-array(rnorm(n*p),dim=c(n,p)); # data-matrix 
Sigma=cov(X); # sample covariance matrix

q<-max(abs(Sigma[row(Sigma)> col(Sigma)])); 
rho=q*0.7;
B<-dpglasso(Sigma,rho=rho,outer.Maxiter=20,outer.tol=10^-6); 
# uses the default initializations for the covariance and precision matrices


# now solve the problem for a smaller value of rho,
# using the previous solution as warm-start
rho.new=rho*.8;
B.new<-dpglasso(Sigma,X=B$X,invX=B$invX,
rho=rho.new,outer.Maxiter=20,outer.tol=10^-6);