# stat.stability_selection: Importance statistics based on stability selection In knockoff: The Knockoff Filter for Controlled Variable Selection

## Description

Computes the difference statistic

W_j = |Z_j| - |\tilde{Z}_j|

where Z_j and \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.

## Usage

 1 stat.stability_selection(X, X_k, y, fitfun = stabs::lars.lasso, ...) 

## Arguments

 X n-by-p matrix of original variables. X_k n-by-p matrix of knockoff variables. y response vector (length n) 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::'. ... additional arguments specific to 'stabs' (see Details).

## Details

This function uses the 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 lars.lasso.

For a complete list of the available additional arguments, see stabsel.

## Value

A vector of statistics W of length p.

Other statistics: stat.forward_selection(), stat.glmnet_coefdiff(), stat.glmnet_lambdadiff(), stat.lasso_coefdiff_bin(), stat.lasso_coefdiff(), stat.lasso_lambdadiff_bin(), stat.lasso_lambdadiff(), stat.random_forest(), stat.sqrt_lasso()
  1 2 3 4 5 6 7 8 9 10 11 12 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)