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```
#' Importance statistics based on stability selection
#'
#' Computes the difference statistic
#' \deqn{W_j = |Z_j| - |\tilde{Z}_j|}
#' where \eqn{Z_j} and \eqn{\tilde{Z}_j} are measure the importance
#' of the jth variable and its knockoff, respectively, based on the
#' stability of their selection upon subsampling of the data.
#'
#' @param X n-by-p matrix of original variables.
#' @param X_k n-by-p matrix of knockoff variables.
#' @param y response vector (length n)
#' @param fitfun fitfun a function that takes the arguments x, y as above,
#' and additionally the number of variables to include in each model q.
#' The function then needs to fit the model and to return a logical vector
#' that indicates which variable was selected (among the q selected variables).
#' The name of the function should be prefixed by 'stabs::'.
#' @param ... additional arguments specific to 'stabs' (see Details).
#' @return A vector of statistics \eqn{W} of length p.
#'
#' @details This function uses the \code{stabs} package to compute
#' variable selection stability. The selection stability of the j-th
#' variable is defined as its probability of being selected upon random
#' subsampling of the data. The default method for selecting variables
#' in each subsampled dataset is \code{\link[stabs]{lars.lasso}}.
#'
#' For a complete list of the available additional arguments, see \code{\link[stabs]{stabsel}}.
#'
#' @family statistics
#'
#' @examples
#' p=50; n=50; k=15
#' mu = rep(0,p); Sigma = diag(p)
#' X = matrix(rnorm(n*p),n)
#' nonzero = sample(p, k)
#' beta = 3.5 * (1:p %in% nonzero)
#' y = X %*% beta + rnorm(n)
#' knockoffs = function(X) create.gaussian(X, mu, Sigma)
#'
#' # Basic usage with default arguments
#' result = knockoff.filter(X, y, knockoffs=knockoffs,
#' statistic=stat.stability_selection)
#' print(result$selected)
#'
#'
#' @rdname stat.stability_selection
#' @export
stat.stability_selection <- function(X, X_k, y, fitfun = stabs::lars.lasso, ...) {
if (!requireNamespace('stabs', quietly=T))
stop('stabs is not installed', call.=F)
if (!is.vector(y)) {
stop('Knockoff statistic stat.stability_selection requires the input y to be a vector')
}
# Randomly swap columns of X and Xk
swap = rbinom(ncol(X),1,0.5)
swap.M = matrix(swap,nrow=nrow(X),ncol=length(swap),byrow=TRUE)
X.swap = X * (1-swap.M) + X_k * swap.M
Xk.swap = X * swap.M + X_k * (1-swap.M)
# Compute statistics
Z = stability_selection_importance(cbind(X.swap, Xk.swap), y, fitfun=fitfun, ...)
p = ncol(X)
orig = 1:p
W = abs(Z[orig]) - abs(Z[orig+p])
# Correct for swapping of columns of X and Xk
W = W * (1-2*swap)
}
#' Stability selection
#'
#' Perform variable selection with stability selection
#'
#' @param X matrix of predictors
#' @param y response vector
#' @return vector with jth component the selection probability of variable j
#'
#' @keywords internal
stability_selection_importance <- function(X, y, ...) {
X = scale(X)
if (!methods::hasArg(cutoff) ) {
cutoff = 0.75
}
if (!methods::hasArg(PFER) ) {
PFER = 1
}
stabFit = stabs::stabsel(X, y, cutoff=cutoff, PFER=PFER, ...)
rowMeans(unname(stabFit$phat))
}
```

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