CONESTA solver.

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).

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.

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 \(X\).

See also

mglasso for the MGLasso model estimation.

Examples

# \donttest{
install_conesta()
#> mglasso requires the r-reticulate virtual environment. Attempting to create...
#> Using Python: /usr/bin/python3.8
#> Creating virtual environment 'r-reticulate' ... 
#> + '/usr/bin/python3.8' -m venv '/home/runner/.virtualenvs/r-reticulate'
#> Done!
#> Installing packages: 'pip', 'wheel', 'setuptools', 'numpy'
#> + '/home/runner/.virtualenvs/r-reticulate/bin/python' -m pip install --upgrade 'pip' 'wheel' 'setuptools' 'numpy'
#> Virtual environment 'r-reticulate' successfully created.
#> Using virtual environment 'r-reticulate' ...
#> + '/home/runner/.virtualenvs/r-reticulate/bin/python' -m pip install --upgrade 'scipy == 1.7.1' 'scikit-learn' 'six' 'matplotlib'
#> Installing pylearn-parsimony
#> pylearn-parsimony is installed.
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
#> 4 x 4 sparse Matrix of class "dgCMatrix"
#>                         
#> [1,] 1.00 0.85 .    .   
#> [2,] 0.85 1.00 .    .   
#> [3,] .    .    1.00 0.85
#> [4,] .    .    0.85 1.00
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)
# }