R/cv.saenet.R

In umich-cphds/minet: Variable Selection for Multiply Imputed Data

#' Cross Validated Multiple Imputation Stacked Adaptive Elastic Net
#'
#' Does k-fold cross-validation for \code{saenet}, and returns optimal values
#' for lambda and alpha.
#'
#' \code{cv.saenet} works by stacking the multiply imputed data into a single
#' matrix and running a weighted adaptive elastic net on it. Simulations suggest
#' that the "stacked" objective function approaches tend to be more
#' computationally efficient and have better estimation and selection
#' properties.
#'
#' Due to stacking, the automatically generated \code{lambda} sequence
#' \code{cv.saenet} generates may end up underestimating \code{lambda.max}, and
#' thus the degrees of freedom  may be nonzero at the first lambda value.
#' @param x A length \code{m} list of \code{n * p} numeric matrices. No matrix
#'     should contain an intercept, or any missing values
#' @param y A length \code{m} list of length \code{n} numeric response vectors.
#'     No vector should contain missing values
#' @param pf Penalty factor of length \code{p}. Can be used to differentially
#'     penalize certain variables. 0 indicates to not penalize the covariate
#' @param adWeight Numeric vector of length p representing the adaptive weights
#'     for the L1 penalty
#' @param weights Numeric vector of length n containing the proportion observed
#'     (non-missing) for each row in the un-imputed data.
#' @param family The type of response. "gaussian" implies a continuous response
#'     and "binomial" implies a binary response. Default is "gaussian".
#' @param alpha Elastic net parameter. Can be a vector to cross validate over.
#'     Default is 1
#' @param nlambda Length of automatically generated "lambda" sequence. If
#'     "lambda" is non NULL, "nlambda" is ignored. Default is 100
#' @param lambda.min.ratio Ratio that determines the minimum value of "lambda"
#'     when automatically generating a "lambda" sequence. If "lambda" is not
#'     NULL, "lambda.min.ratio" is ignored. Default is 1e-3
#' @param lambda Optional numeric vector of lambdas to fit. If NULL,
#'    \code{galasso} will automatically generate a lambda sequence based off
#'    of \code{nlambda} and \code{lambda.min.ratio}. Default is NULL
#' @param nfolds Number of foldid to use for cross validation. Default is 5,
#'     minimum is 3
#' @param foldid an optional length \code{n} vector of values between 1 and
#     "nfold" identifying what fold each observation is in. Default is NULL and
#'     \code{cv.galasso} will automatically generate folds
#' @param maxit Maximum number of iterations to run. Default is 1000
#' @param eps Tolerance for convergence. Default is 1e-5
#' @returns An object of type "cv.saenet" with 9 elements:
#' \describe{
#' \item{call}{The call that generated the output.}
#' \item{lambda}{Sequence of lambdas fit.}
#' \item{cvm}{Average cross validation error for each lambda and alpha. For
#'            family = "gaussian", "cvm" corresponds to mean squared error,
#'            and for binomial "cvm" corresponds to deviance.}
#' \item{cvse}{Standard error of "cvm".}
#' \item{saenet.fit}{A "saenet" object fit to the full data.}
#' \item{lambda.min}{The lambda value for the model with the minimum cross
#'                   validation error.}
#' \item{lambda.1se}{The lambda value for the  sparsest model within one
#'                   standard error of the minimum cross validation error.}
#' \item{alpha.min}{The alpha value for the model with the minimum cross
#'                   validation error.}
#' \item{alpha.1se}{The alpha value for the  sparsest model within one
#'                   standard error of the minimum cross validation error.}
#' \item{df}{The number of nonzero coefficients for each value of lambda and alpha.}
#' }
#' @references
#' Du, J., Boss, J., Han, P., Beesley, L. J., Kleinsasser, M., Goutman, S. A., ... 
#' & Mukherjee, B. (2022). Variable selection with multiply-imputed datasets: 
#' choosing between stacked and grouped methods. Journal of Computational and 
#' Graphical Statistics, 31(4), 1063-1075. <doi:10.1080/10618600.2022.2035739>
#' 
#' @examples
#' \donttest{
#' library(miselect)
#' library(mice)
#'
#' set.seed(48109)
#'
#' # Using the mice defaults for sake of example only.
#' mids <- mice(miselect.df, m = 5, printFlag = FALSE)
#' dfs <- lapply(1:5, function(i) complete(mids, action = i))
#'
#' # Generate list of imputed design matrices and imputed responses
#' x <- list()
#' y <- list()
#' for (i in 1:5) {
#'     x[[i]] <- as.matrix(dfs[[i]][, paste0("X", 1:20)])
#'     y[[i]] <- dfs[[i]]$Y
#' }
#'
#' # Calculate observational weights
#' weights  <- 1 - rowMeans(is.na(miselect.df))
#' pf       <- rep(1, 20)
#' adWeight <- rep(1, 20)
#'
#' # Since 'Y' is a binary variable, we use 'family = "binomial"'
#' fit <- cv.saenet(x, y, pf, adWeight, weights, family = "binomial")
#'
#' # By default 'coef' returns the betas for (lambda.min , alpha.min)
#' coef(fit)
#' }
#'
#' # You can also cross validate over alpha
#' \donttest{
#' fit <- cv.saenet(x, y, pf, adWeight, weights, family = "binomial",
#'                  alpha = c(.5, 1))
#' # Get selected variables from the 1 standard error rule
#' coef(fit, lambda = fit$lambda.1se, alpha = fit$alpha.1se)
#'
#' }
#' @export
cv.saenet <- function(x, y, pf, adWeight, weights, family = c("gaussian", "binomial"),
                      alpha = 1, nlambda = 100, lambda.min.ratio =
                        ifelse(isTRUE(all.equal(adWeight, rep(1, p))), 1e-3, 1e-6),
                      lambda = NULL, nfolds = 5, foldid = NULL, maxit = 1000,
                      eps = 1e-5)
{
  call <- match.call()
  
  if (!is.list(x))
    stop("'x' should be a list of numeric matrices.")
  if (any(sapply(x, function(.x) !is.matrix(.x) || !is.numeric(.x))))
    stop("Every 'x' should be a numeric matrix.")
  
  dim <- dim(x[[1]])
  n <- dim[1]
  p <- dim[2]
  m <- length(x)
  
  if (!is.numeric(nfolds) || length(nfolds) > 1)
    stop("'nfolds' should a be single number.")
  
  if (!is.null(foldid))
    if (!is.numeric(foldid) || length(foldid) != length(y[[1]]))
      stop("'nfolds' should a be single number.")
  
  fit <- saenet(x, y, pf, adWeight, weights, family, alpha, nlambda,
                lambda.min.ratio, lambda, maxit, eps)
  
  X <- do.call("rbind", x)
  Y <- do.call("c", y)
  
  weights <- rep(weights / m , m)
  
  if (!is.null(foldid)) {
    if (!is.numeric(foldid) || !is.vector(foldid) || length(foldid) != n)
      stop("'foldid' must be length n numeric vector.")
    nfolds <- max(foldid)
  } else {
    r     <- n %% nfolds
    q     <- (n - r) / nfolds
    if(r == 0) {
      foldid = rep(seq(nfolds), q)
    } else {
      foldid = c(rep(seq(nfolds), q), seq(r))
    }
    foldid <- sample(foldid, n)
    foldid <- rep(foldid, m)
  }
  if (nfolds < 3)
    stop("'nfolds' must be bigger than 3.")
  
  lambda  <- fit$lambda
  nlambda <- length(lambda)
  X.scaled <- scale(X, scale = apply(X, 2, function(.X) stats::sd(.X) * sqrt(m)))
  
  cvm  <- array(0, c(nlambda, length(alpha), nfolds))
  cvse <- matrix(nlambda, length(alpha))
  for (j in seq(nfolds)) {
    Y.train <- Y[foldid != j]
    X.train <- subset_scaled_matrix(X.scaled, foldid != j)
    w.train <- weights[foldid != j]
    
    X.test  <- X[foldid == j, , drop = F]
    Y.test  <- Y[foldid == j]
    w.test <- weights[foldid == j]
    
    cv.fit <- switch(match.arg(family),
                     gaussian = fit.saenet.gaussian(X.train, Y.train, n, p, m, w.train,
                                                    nlambda, lambda, alpha, pf, adWeight,
                                                    maxit, eps),
                     binomial = fit.saenet.binomial(X.train, Y.train, n, p, m, w.train,
                                                    nlambda, lambda, alpha, pf, adWeight,
                                                    maxit, eps)
    )
    
    cvm[,, j] <- cv.saenet.err(cv.fit, X.test, Y.test, w.test, m)
  }
  
  cvse <- apply(cvm, c(1, 2), stats::sd) / sqrt(nfolds)
  cvm  <- apply(cvm, c(1, 2), mean)
  
  min.id = which(cvm == min(cvm), arr.ind = TRUE)
  se = cvse[min.id[1], min.id[2]]
  range = min(cvm) + se
  
  all.id = which(cvm < range, arr.ind = TRUE)
  lambda.seq = lambda[all.id[, 1]]
  alpha.seq = alpha[all.id[, 2]]
  L1 = lambda.seq * alpha.seq
  L1.max.id = which(L1 == max(L1))
  lambda.1se.id = all.id[L1.max.id, 1]
  alpha.1se.id = all.id[L1.max.id, 2]
  lambda.1se = lambda[lambda.1se.id]
  alpha.1se = alpha[alpha.1se.id]
  i.min    <- which.min(apply(cvm, 1, min))
  j.min    <- which.min(apply(cvm, 2, min))
  
  lambda.min <- fit$lambda[i.min]
  alpha.min <- fit$alpha[j.min]
  
  structure(list(call = call, lambda = fit$lambda, alpha = alpha, cvm = cvm,
                 cvse = cvse, saenet.fit = fit, 
                 lambda.min = lambda.min,
                 alpha.min = alpha.min, 
                 lambda.1se = lambda.1se, alpha.1se =
                 alpha.1se, df = fit$df), class = "cv.saenet")
}


cv.saenet.err <- function(cv.fit, X.test, Y.test, w.test, m)
{
  nalpha <- length(cv.fit$alpha)
  nlambda <- length(cv.fit$lambda)
  cvm <- matrix(0, nlambda, nalpha)
  
  for (j in seq(nlambda)) {
    for (i in seq(nalpha)) {
      coef <- cv.fit$coef[j, i,]
      coef0 <- coef[1]
      coef  <- coef[-1]
      if ("saenet.gaussian" %in% class(cv.fit)) {
        mse <- m * mean((Y.test - X.test %*% coef - coef0) ^ 2 * w.test)
        cvm[j, i] <- mse
      }
      else {
        eta <- X.test %*% coef + coef0
        dev <-  w.test * (Y.test * eta - log(1 + exp(eta)))
        cvm[j, i] <- -2 * m * mean(dev)
      }
    }
  }
  cvm
}


#' Print cv.saenet Objects
#'
#' \code{print.cv.saenet} print the fit and returns it invisibly.
#' @param x An object of type "cv.saenet" to print
#' @param ... Further arguments passed to or from other methods
#' @export
print.cv.saenet <- function(x, ...)
{
  nl <- length(x$lambda)
  na <- length(x$alpha)
  
  cvm <- x$cvm
  dimnames(cvm) <- list(paste0("l.", seq(nl)), paste0("a.", seq(na)))
  cat("'cv.saenet' fit:\n")
  print(x$call)
  cat("Average cross validation error for each (lambda, alpha)\n")
  print(cvm)
  cat("(lambda, alpha) min:\n")
  cat("(", x$lambda.min, ", ", x$alpha.min, ")\n", sep = "")
  cat("(lambda, alpha) 1 SE:\n")
  cat("(", x$lambda.1se, ", ", x$alpha.1se, ")\n", sep = "")
  invisible(x)
}