# stat.lasso_coefdiff: Importance statistics based the lasso with cross-validation In knockoff: The Knockoff Filter for Controlled Variable Selection

## Description

Fits a linear regression model via penalized maximum likelihood and cross-validation. Then, compute the difference statistic

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

where Z_j and \tilde{Z}_j are the coefficient estimates for the jth variable and its knockoff, respectively. The value of the regularization parameter λ is selected by cross-validation and computed with glmnet.

## Usage

 1 stat.lasso_coefdiff(X, X_k, y, cores = 2, ...) 

## Arguments

 X n-by-p matrix of original variables. X_k n-by-p matrix of knockoff variables. y vector of length n, containing the response variables. It should be numeric cores Number of cores used to compute the statistics by running cv.glmnet. If not specified, the number of cores is set to approximately half of the number of cores detected by the parallel package. ... additional arguments specific to glmnet (see Details).

## Details

This function uses the glmnet package to fit the lasso path and is a wrapper around the more general stat.glmnet_coefdiff.

The statistics W_j are constructed by taking the difference between the coefficient of the j-th variable and its knockoff.

By default, the value of the regularization parameter is chosen by 10-fold cross-validation.

The optional nlambda parameter can be used to control the granularity of the grid of λ's. The default value of nlambda is 500, where p is the number of columns of X.

Unless a lambda sequence is provided by the user, this function generates it on a log-linear scale before calling 'glmnet' (default 'nlambda': 500).

For a complete list of the available additional arguments, see cv.glmnet and glmnet.

## 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_lambdadiff_bin(), stat.lasso_lambdadiff(), stat.random_forest(), stat.sqrt_lasso(), stat.stability_selection()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 p=200; n=100; 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.lasso_coefdiff) print(result$selected) # Advanced usage with custom arguments foo = stat.lasso_coefdiff k_stat = function(X, X_k, y) foo(X, X_k, y, nlambda=200) result = knockoff.filter(X, y, knockoffs=knockoffs, statistic=k_stat) print(result$selected)