cv_MADMMplasso: Carries out cross-validation for a MADMMplasso model over a...

In MADMMplasso: Multi Variate Multi Response ADMM with Interaction Effects

Carries out cross-validation for a MADMMplasso model over a path of regularization values

Description

Carries out cross-validation for a MADMMplasso model over a path of regularization values

Usage

cv_MADMMplasso(
  fit,
  nfolds,
  X,
  Z,
  y,
  alpha = 0.5,
  lambda = fit$Lambdas,
  max_it = 50000,
  e.abs = 0.001,
  e.rel = 0.001,
  nlambda,
  rho = 5,
  my_print = FALSE,
  alph = 1,
  foldid = NULL,
  pal = cl == 1L,
  gg = c(7, 0.5),
  TT,
  tol = 1e-04,
  cl = 1L,
  legacy = FALSE
)

Arguments

fit	object returned by the MADMMplasso function
nfolds	number of cross-validation folds
X	N by p matrix of predictors
Z	N by K matrix of modifying variables. The elements of Z may represent quantitative or categorical variables, or a mixture of the two. Categorical variables should be coded by 0-1 dummy variables: for a k-level variable, one can use either k or k-1 dummy variables.
y	N by D matrix of responses. The X and Z variables are centered in the function. We recommend that X and Z also be standardized before the call
alpha	mixing parameter. When the goal is to include more interactions, alpha should be very small and vice versa.
lambda	user specified lambda_3 values.
max_it	maximum number of iterations in loop for one lambda during the ADMM optimization
e.abs	absolute error for the ADMM
e.rel	relative error for the ADMM
nlambda	number of lambda_3 values desired. Similar to maxgrid but can have a value less than or equal to maxgrid.
rho	the Lagrange variable for the ADMM. This value is updated during the ADMM call based on a certain condition.
my_print	Should information form each ADMM iteration be printed along the way? This prints the dual and primal residuals
alph	an overrelaxation parameter in [1, 1.8]. The implementation is borrowed from Stephen Boyd's MATLAB code
foldid	vector with values in 1:K, indicating folds for K-fold CV. Default NULL
pal	Should the lapply function be applied for an alternative to parallelization.
gg	penalty term for the tree structure. This is a 2×2 matrix values in the first row representing the maximum to the minimum values for lambda_1 and the second row representing the maximum to the minimum values for lambda_2. In the current setting, we set both maximum and the minimum to be same because cross validation is not carried across the lambda_1 and lambda_2. However, setting different values will work during the model fit.
TT	The results from the hierarchical clustering of the response matrix. This should same as the parameter tree used during the MADMMplasso call.
tol	threshold for the non-zero coefficients
cl	The number of CPUs to be used for parallel processing
legacy	If TRUE, use the R version of the algorithm

Value

results containing the CV values

Examples

# Train the model
# generate some data
set.seed(1235)
N <- 100
p <- 50
nz <- 4
K <- nz
X <- matrix(rnorm(n = N * p), nrow = N, ncol = p)
mx <- colMeans(X)
sx <- sqrt(apply(X, 2, var))
X <- scale(X, mx, sx)
X <- matrix(as.numeric(X), N, p)
Z <- matrix(rnorm(N * nz), N, nz)
mz <- colMeans(Z)
sz <- sqrt(apply(Z, 2, var))
Z <- scale(Z, mz, sz)
beta_1 <- rep(x = 0, times = p)
beta_2 <- rep(x = 0, times = p)
beta_3 <- rep(x = 0, times = p)
beta_4 <- rep(x = 0, times = p)
beta_5 <- rep(x = 0, times = p)
beta_6 <- rep(x = 0, times = p)

beta_1[1:5] <- c(2, 2, 2, 2, 2)
beta_2[1:5] <- c(2, 2, 2, 2, 2)
beta_3[6:10] <- c(2, 2, 2, -2, -2)
beta_4[6:10] <- c(2, 2, 2, -2, -2)
beta_5[11:15] <- c(-2, -2, -2, -2, -2)
beta_6[11:15] <- c(-2, -2, -2, -2, -2)

Beta <- cbind(beta_1, beta_2, beta_3, beta_4, beta_5, beta_6)
colnames(Beta) <- c(1:6)

theta <- array(0, c(p, K, 6))
theta[1, 1, 1] <- 2
theta[3, 2, 1] <- 2
theta[4, 3, 1] <- -2
theta[5, 4, 1] <- -2
theta[1, 1, 2] <- 2
theta[3, 2, 2] <- 2
theta[4, 3, 2] <- -2
theta[5, 4, 2] <- -2
theta[6, 1, 3] <- 2
theta[8, 2, 3] <- 2
theta[9, 3, 3] <- -2
theta[10, 4, 3] <- -2
theta[6, 1, 4] <- 2
theta[8, 2, 4] <- 2
theta[9, 3, 4] <- -2
theta[10, 4, 4] <- -2
theta[11, 1, 5] <- 2
theta[13, 2, 5] <- 2
theta[14, 3, 5] <- -2
theta[15, 4, 5] <- -2
theta[11, 1, 6] <- 2
theta[13, 2, 6] <- 2
theta[14, 3, 6] <- -2
theta[15, 4, 6] <- -2

pliable <- matrix(0, N, 6)
for (e in 1:6) {
  pliable[, e] <- compute_pliable(X, Z, theta[, , e])
}

esd <- diag(6)
e <- MASS::mvrnorm(N, mu = rep(0, 6), Sigma = esd)
y_train <- X %*% Beta + pliable + e
y <- y_train

colnames(y) <- c(paste("y", 1:(ncol(y)), sep = ""))
TT <- tree_parms(y)
plot(TT$h_clust)
gg1 <- matrix(0, 2, 2)
gg1[1, ] <- c(0.02, 0.02)
gg1[2, ] <- c(0.02, 0.02)
nlambda <- 3
e.abs <- 1E-3
e.rel <- 1E-1
alpha <- .2
tol <- 1E-2
fit <- MADMMplasso(
  X, Z, y, alpha = alpha, my_lambda = NULL, lambda_min = 0.001, max_it = 100,
  e.abs = e.abs, e.rel = e.rel, maxgrid = nlambda, nlambda = nlambda, rho = 5,
  tree = TT, my_print = FALSE, alph = 1, gg = gg1, tol = tol, cl = 2L
)
cv_admp <- cv_MADMMplasso(
  fit, nfolds = 5, X, Z, y, alpha = alpha, lambda = fit$Lambdas, max_it = 100,
  e.abs = e.abs, e.rel = e.rel, nlambda, rho = 5, my_print = FALSE, alph = 1,
  foldid = NULL, gg = fit$gg, TT = TT, tol = tol
)
plot(cv_admp)

MADMMplasso documentation built on April 3, 2025, 10:53 p.m.