lagrangian: lagrangian function

In desanou/mglasso: Multiscale Graphical Lasso

lagrangian function

Description

Beta and X must have the same number of variables

Beta and X must have the same number of variables

Usage

lagrangian(Beta, X, lambda1 = 0, lambda2 = 0)

lagrangian(Beta, X, lambda1 = 0, lambda2 = 0)

Arguments

Beta	numeric matrix. In rows, regression vectors coefficients following of node-wise regression. diag(Beta) = 0
X	numeric matrix. Data with variables in columns.
lambda1	numeric scalar. Lasso penalization parameter.
lambda2	numeric scalar. Fused-group Lasso penalization parameter.

Value

numeric scalar. The lagrangian

numeric scalar. The lagrangian

Examples

## Generation of K block partitions
n = 50
K = 3
p = 6
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 <- bdiag(blocs)
set.seed(11)
X <- rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

## Initialization for Beta
Beta1 <- matrix(0, nrow = p, ncol = p)
for(i in 1:p){
  Beta1[i,-i] <- solve(t(X[,-i])%*%X[,-i]) %*% t(X[,-i]) %*% X[,i]
  }
lagrangian(Beta, X, 0, 0)

## Generation of K block partitions
n = 50
K = 3
p = 6
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 <- bdiag(blocs)
set.seed(11)
X <- rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

## Initialization for Beta
Beta1 <- matrix(0, nrow = p, ncol = p)
for(i in 1:p){
  Beta1[i,-i] <- solve(t(X[,-i])%*%X[,-i]) %*% t(X[,-i]) %*% X[,i]
  }
lagrangian(Beta, X, 0, 0)

desanou/mglasso documentation built on July 1, 2023, 6:39 a.m.