# MFKnockoffs.stat.stability_selection: Stability selection statistics for MFKnockoffs In MFKnockoffs: Model-Free 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 2 MFKnockoffs.stat.stability_selection(X, X_k, y, fitfun = stabs::glmnet.lasso, ...) 

## Arguments

 X original design matrix (size n-by-p) X_k knockoff matrix (size n-by-p) 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 stabs::glmnet.lasso_maxCoef.

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

## Value

A vector of statistics W (length p)

Other statistics for knockoffs: MFKnockoffs.stat.forward_selection, MFKnockoffs.stat.glmnet_coef_difference, MFKnockoffs.stat.glmnet_lambda_difference, MFKnockoffs.stat.lasso_coef_difference_bin, MFKnockoffs.stat.lasso_coef_difference, MFKnockoffs.stat.lasso_lambda_difference_bin, MFKnockoffs.stat.lasso_lambda_difference, MFKnockoffs.stat.random_forest, MFKnockoffs.stat.sqrt_lasso
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 p=100; n=200; 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) MFKnockoffs.create.gaussian(X, mu, Sigma) # Basic usage with default arguments result = MFKnockoffs.filter(X, y, knockoffs=knockoffs, statistic=MFKnockoffs.stat.stability_selection) print(result$selected) # Advanced usage with custom arguments foo = MFKnockoffs.stat.stability_selection k_stat = function(X, X_k, y) foo(X, X_k, y, fitfun=stabs::lars.lasso) result = MFKnockoffs.filter(X, y, knockoffs=knockoffs, statistic=k_stat) print(result$selected)