msaenet: Multi-Step Adaptive Estimation Methods for Sparse Regressions

Documented in msaenet

#' Multi-Step Adaptive Elastic-Net
#'
#' Multi-Step Adaptive Elastic-Net
#'
#' @param x Data matrix.
#' @param y Response vector if \code{family} is \code{"gaussian"},
#' \code{"binomial"}, or \code{"poisson"}. If \code{family} is
#' \code{"cox"}, a response matrix created by \code{\link[survival]{Surv}}.
#' @param family Model family, can be \code{"gaussian"},
#' \code{"binomial"}, \code{"poisson"}, or \code{"cox"}.
#' @param init Type of the penalty used in the initial
#' estimation step. Can be \code{"enet"} or \code{"ridge"}.
#' See \code{\link[glmnet]{glmnet}} for details.
#' @param alphas Vector of candidate \code{alpha}s to use in
#' \code{\link[glmnet]{cv.glmnet}}.
#' @param tune Parameter tuning method for each estimation step.
#' Possible options are \code{"cv"}, \code{"ebic"}, \code{"bic"},
#' and \code{"aic"}. Default is \code{"cv"}.
#' @param nfolds Fold numbers of cross-validation when \code{tune = "cv"}.
#' @param rule Lambda selection criterion when \code{tune = "cv"},
#' can be \code{"lambda.min"} or \code{"lambda.1se"}.
#' See \code{\link[glmnet]{cv.glmnet}} for details.
#' @param ebic.gamma Parameter for Extended BIC penalizing
#' size of the model space when \code{tune = "ebic"},
#' default is \code{1}. For details, see Chen and Chen (2008).
#' @param nsteps Maximum number of adaptive estimation steps.
#' At least \code{2}, assuming adaptive elastic-net has only
#' one adaptive estimation step.
#' @param tune.nsteps Optimal step number selection method
#' (aggregate the optimal model from the each step and compare).
#' Options include \code{"max"} (select the final-step model directly),
#' or compare these models using \code{"ebic"}, \code{"bic"}, or \code{"aic"}.
#' Default is \code{"max"}.
#' @param ebic.gamma.nsteps Parameter for Extended BIC penalizing
#' size of the model space when \code{tune.nsteps = "ebic"},
#' default is \code{1}.
#' @param scale Scaling factor for adaptive weights:
#' \code{weights = coefficients^(-scale)}.
#' @param lower.limits Lower limits for coefficients.
#' Default is \code{-Inf}. For details, see \code{\link[glmnet]{glmnet}}.
#' @param upper.limits Upper limits for coefficients.
#' Default is \code{Inf}. For details, see \code{\link[glmnet]{glmnet}}.
#' @param 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 \code{rep(1, ncol(x))}.
#' @param seed Random seed for cross-validation fold division.
#' @param parallel Logical. Enable parallel parameter tuning or not,
#' default is \code{FALSE}. To enable parallel tuning, load the
#' \code{doParallel} package and run \code{registerDoParallel()}
#' with the number of CPU cores before calling this function.
#' @param verbose Should we print out the estimation progress?
#'
#' @return List of model coefficients, \code{glmnet} model object,
#' and the optimal parameter set.
#'
#' @author Nan Xiao <\url{https://nanx.me}>
#'
#' @references
#' Nan Xiao and Qing-Song Xu. (2015). Multi-step adaptive elastic-net:
#' reducing false positives in high-dimensional variable selection.
#' \emph{Journal of Statistical Computation and Simulation} 85(18), 3755--3765.
#'
#' @importFrom glmnet glmnet
#' @importFrom Matrix Matrix
#'
#' @export msaenet
#'
#' @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)
#' msaenet.nzv(msaenet.fit)
#' msaenet.fp(msaenet.fit, 1:5)
#' msaenet.tp(msaenet.fit, 1:5)
#' msaenet.pred <- predict(msaenet.fit, dat$x.te)
#' msaenet.rmse(dat$y.te, msaenet.pred)
#' plot(msaenet.fit)
msaenet <- function(
    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) {
  if (nsteps < 2L) stop("`nsteps` must be an integer >= 2.", call. = FALSE)

  family <- match.arg(family)
  init <- match.arg(init)
  tune <- match.arg(tune)
  rule <- match.arg(rule)
  tune.nsteps <- match.arg(tune.nsteps)
  call <- match.call()

  best.alphas <- rep(NA, nsteps + 1L)
  best.lambdas <- rep(NA, nsteps + 1L)
  step.criterion <- rep(NA, nsteps + 1L)
  beta.list <- vector("list", nsteps + 1L)
  model.list <- vector("list", nsteps + 1L)
  adapen.list <- vector("list", nsteps)

  if (verbose) cat("Starting step 1 ...\n")

  if (init == "enet") {
    model.cv <- msaenet.tune.glmnet(
      x = x, y = y, family = family,
      alphas = alphas,
      tune = tune,
      nfolds = nfolds, rule = rule,
      ebic.gamma = ebic.gamma,
      lower.limits = lower.limits,
      upper.limits = upper.limits,
      penalty.factor = penalty.factor.init,
      seed = seed, parallel = parallel
    )
  }

  if (init == "ridge") {
    model.cv <- msaenet.tune.glmnet(
      x = x, y = y, family = family,
      alphas = 0,
      tune = tune,
      nfolds = nfolds, rule = rule,
      ebic.gamma = ebic.gamma,
      lower.limits = lower.limits,
      upper.limits = upper.limits,
      penalty.factor = penalty.factor.init,
      seed = seed, parallel = parallel
    )
  }

  best.alphas[[1L]] <- model.cv$"best.alpha"
  best.lambdas[[1L]] <- model.cv$"best.lambda"
  step.criterion[[1L]] <- model.cv$"step.criterion"

  model.list[[1L]] <- glmnet(
    x = x, y = y, family = family,
    alpha = best.alphas[[1L]],
    lambda = best.lambdas[[1L]],
    lower.limits = lower.limits,
    upper.limits = upper.limits,
    penalty.factor = penalty.factor.init
  )

  if (.df(model.list[[1L]]) < 0.5) stop(message.null.model, call. = FALSE)

  bhat <- as.matrix(model.list[[1L]][["beta"]])
  if (all(bhat == 0)) bhat <- rep(.Machine$double.eps * 2, length(bhat))
  beta.list[[1L]] <- bhat

  # MSAEnet steps
  for (i in 1L:nsteps) {
    adpen.raw <- (pmax(abs(beta.list[[i]]), .Machine$double.eps))^(-scale)
    adapen.list[[i]] <- as.vector(adpen.raw)
    adpen.name <- rownames(adpen.raw)
    names(adapen.list[[i]]) <- adpen.name

    if (verbose) cat("Starting step", i + 1, "...\n")

    model.cv <- msaenet.tune.glmnet(
      x = x, y = y, family = family,
      alphas = alphas,
      tune = tune,
      nfolds = nfolds, rule = rule,
      ebic.gamma = ebic.gamma,
      lower.limits = lower.limits,
      upper.limits = upper.limits,
      seed = seed + i, parallel = parallel,
      penalty.factor = adapen.list[[i]]
    )

    best.alphas[[i + 1L]] <- model.cv$"best.alpha"
    best.lambdas[[i + 1L]] <- model.cv$"best.lambda"
    step.criterion[[i + 1L]] <- model.cv$"step.criterion"

    model.list[[i + 1L]] <- glmnet(
      x = x, y = y, family = family,
      alpha = best.alphas[[i + 1L]],
      lambda = best.lambdas[[i + 1L]],
      lower.limits = lower.limits,
      upper.limits = upper.limits,
      penalty.factor = adapen.list[[i]]
    )

    if (.df(model.list[[i + 1L]]) < 0.5) stop(message.null.model, call. = FALSE)

    bhat <- as.matrix(model.list[[i + 1L]][["beta"]])
    if (all(bhat == 0)) bhat <- rep(.Machine$double.eps * 2, length(bhat))
    beta.list[[i + 1L]] <- bhat
  }

  # select optimal step
  post.ics <- msaenet.tune.nsteps.glmnet(
    model.list, tune.nsteps, ebic.gamma.nsteps
  )

  best.step <- post.ics$"best.step"
  post.criterion <- post.ics$"ics"

  msaenet.model <- list(
    "beta" = Matrix(beta.list[[best.step]], sparse = TRUE),
    "model" = model.list[[best.step]],
    "best.step" = best.step,
    "best.alphas" = best.alphas,
    "best.lambdas" = best.lambdas,
    "step.criterion" = step.criterion,
    "post.criterion" = post.criterion,
    "beta.list" = beta.list,
    "model.list" = model.list,
    "adapen.list" = adapen.list,
    "seed" = seed,
    "call" = call
  )

  class(msaenet.model) <- c("msaenet", "msaenet.msaenet")
  msaenet.model
}