conesta {mglasso}

CONESTA solver.

Description

Solve the MGLasso optimization problem using CONESTA algorithm. Interface to the pylearn.parsimony python library.

Usage

conesta(
  X,
  lam1,
  lam2,
  beta_warm = c(0),
  type_ = "initial",
  W_ = NULL,
  mean_ = FALSE,
  max_iter_ = 10000,
  prec_ = 0.01
)

Arguments

X

Data matrix nxp.

lam1

Sparsity penalty.

lam2

Total variation penalty.

beta_warm

Warm initialization vector.

type_

Character scalar. By default set to initial version which doesn't use weights

W_

Weights matrix for total variation penalties.

mean_

Logical scalar. If TRUE weights the optimization function by the inverse of sample size.

max_iter_

Numeric scalar. Maximum number of iterations.

prec_

Numeric scalar. Tolerance for the stopping criterion (duality gap).

Details

COntinuation with NEsterov smoothing in a Shrinkage-Thresholding Algorithm (CONESTA, Hadj-Selem et al. 2018) doi:10.1109/TMI.2018.2829802 is an algorithm design for solving optimization problems including group-wise penalties. This function is an interface with the python solver. The MGLasso problem is first reformulated in a problem of the form

argmin 1/2 ||Y - \tilde{X} \tilde{\beta}||_2^2 + \lambda_1 ||\tilde{\beta}||_1 + \lambda_2 \sum_{i<j} ||\boldsymbol A_{ij} \tilde{\beta}||_2

where vector Y is the vectorized form of matrix X.

Value

Numeric matrix of size pxp. Line k of the matrix represents the coefficients obtained from the L1-L2 penalized regression of variable k on the others.

See Also

mglasso() for the MGLasso model estimation.

Examples

## Not run: # because of installation of external packages during checks
mglasso::install_pylearn_parsimony(envname = "rmglasso", method = "conda")
reticulate::use_condaenv("rmglasso", required = TRUE)
reticulate::py_config()
n = 30
K = 2
p = 4
rho = 0.85
blocs <- list()
for (j in 1:K) {
 bloc <- matrix(rho, nrow = p/K, ncol = p/K)
   for(i in 1:(p/K)) { bloc[i,i] <- 1 }
   blocs[[j]] <- bloc
   }

mat.covariance <- Matrix::bdiag(blocs)
mat.covariance
set.seed(11)
X <- mvtnorm::rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)
res <- conesta(X, 0.1, 0.1)

## End(Not run)