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

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

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.