# MFKnockoffs.stat.lasso_lambda_signed_max: Penalized linear regression statistics for MFKnockoffs In MFKnockoffs: Model-Free Knockoff Filter for Controlled Variable Selection

## Description

Computes the signed maximum statistic

W_j = \max(Z_j, \tilde{Z}_j) \cdot \mathrm{sgn}(Z_j - \tilde{Z}_j),

where Z_j and \tilde{Z}_j are the maximum values of λ at which the jth variable and its knockoff, respectively, enter the penalized linear regression model.

## Usage

 1 MFKnockoffs.stat.lasso_lambda_signed_max(X, X_k, y, ...) 

## Arguments

 X original design matrix (size n-by-p) X_k knockoff matrix (size n-by-p) y response vector (length n). It should be numeric. ... additional arguments specific to 'glmnet' or 'lars' (see Details)

## Details

This function uses glmnet to compute the regularization path on a fine grid of λ's.

The additional nlambda parameter can be used to control the granularity of the grid of λ values. The default value of nlambda is 100.

Unless a lambda sequence is provided by the user, this function generates it on a log-linear scale before calling 'glmnet' (default 'nlambda': 100).

This function is a wrapper around the more general MFKnockoffs.stat.glmnet_lambda_difference.

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

## Value

A vector of statistics W (length p)

## Examples

  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, knockoff=knockoffs, statistic=MFKnockoffs.stat.lasso_lambda_signed_max) print(result$selected) # Advanced usage with custom arguments foo = MFKnockoffs.stat.lasso_lambda_signed_max k_stat = function(X, X_k, y) foo(X, X_k, y, nlambda=200) result = MFKnockoffs.filter(X, y, knockoffs=knockoffs, statistic=k_stat) print(result$selected) 

MFKnockoffs documentation built on May 2, 2019, 6:33 a.m.