Multi-Step Adaptive Elastic-Net

msaenet(x, y, family = c("gaussian", "binomial", "poisson", "cox"),
  init = c("enet", "ridge"), alphas = seq(0.05, 0.95, 0.05),
  tune = c("cv", "ebic", "bic", "aic"), nfolds = 5L,
  rule = c("lambda.min", "lambda.1se"), ebic.gamma = 1, nsteps = 2L,
  tune.nsteps = c("max", "ebic", "bic", "aic"), ebic.gamma.nsteps = 1,
  scale = 1, lower.limits = -Inf, upper.limits = Inf,
  penalty.factor.init = rep(1, ncol(x)), seed = 1001,
  parallel = FALSE, verbose = FALSE)

Arguments

x

Data matrix.

y

Response vector if family is "gaussian", "binomial", or "poisson". If family is "cox", a response matrix created by Surv.

family

Model family, can be "gaussian", "binomial", "poisson", or "cox".

init

Type of the penalty used in the initial estimation step. Can be "enet" or "ridge". See glmnet for details.

alphas

Vector of candidate alphas to use in cv.glmnet.

tune

Parameter tuning method for each estimation step. Possible options are "cv", "ebic", "bic", and "aic". Default is "cv".

nfolds

Fold numbers of cross-validation when tune = "cv".

rule

Lambda selection criterion when tune = "cv", can be "lambda.min" or "lambda.1se". See cv.glmnet for details.

ebic.gamma

Parameter for Extended BIC penalizing size of the model space when tune = "ebic", default is 1. For details, see Chen and Chen (2008).

nsteps

Maximum number of adaptive estimation steps. At least 2, assuming adaptive elastic-net has only one adaptive estimation step.

tune.nsteps

Optimal step number selection method (aggregate the optimal model from the each step and compare). Options include "max" (select the final-step model directly), or compare these models using "ebic", "bic", or "aic". Default is "max".

ebic.gamma.nsteps

Parameter for Extended BIC penalizing size of the model space when tune.nsteps = "ebic", default is 1.

scale

Scaling factor for adaptive weights: weights = coefficients^(-scale).

lower.limits

Lower limits for coefficients. Default is -Inf. For details, see glmnet.

upper.limits

Upper limits for coefficients. Default is Inf. For details, see glmnet.

penalty.factor.init

The multiplicative factor for the penalty applied to each coefficient in the initial estimation step. This is useful for incorporating prior information about variable weights, for example, emphasizing specific clinical variables. To make certain variables more likely to be selected, assign a smaller value. Default is rep(1, ncol(x)).

seed

Random seed for cross-validation fold division.

parallel

Logical. Enable parallel parameter tuning or not, default is FALSE. To enable parallel tuning, load the doParallel package and run registerDoParallel() with the number of CPU cores before calling this function.

verbose

Should we print out the estimation progress?

Value

List of model coefficients, glmnet model object, and the optimal parameter set.

References

Nan Xiao and Qing-Song Xu. (2015). Multi-step adaptive elastic-net: reducing false positives in high-dimensional variable selection. Journal of Statistical Computation and Simulation 85(18), 3755--3765.

Examples

dat <- msaenet.sim.gaussian( n = 150, p = 500, rho = 0.6, coef = rep(1, 5), snr = 2, p.train = 0.7, seed = 1001 ) msaenet.fit <- msaenet( dat$x.tr, dat$y.tr, alphas = seq(0.2, 0.8, 0.2), nsteps = 3L, seed = 1003 ) print(msaenet.fit)
#> Call: msaenet(x = dat$x.tr, y = dat$y.tr, alphas = seq(0.2, 0.8, 0.2), #> nsteps = 3L, seed = 1003) #> Df %Dev Lambda #> 1 12 0.8149474 9.517421e+14
msaenet.nzv(msaenet.fit)
#> [1] 2 3 4 5 35 114 171 312 379 441 464 500
msaenet.fp(msaenet.fit, 1:5)
#> [1] 8
msaenet.tp(msaenet.fit, 1:5)
#> [1] 4
msaenet.pred <- predict(msaenet.fit, dat$x.te) msaenet.rmse(dat$y.te, msaenet.pred)
#> [1] 2.656733
plot(msaenet.fit)