MFKnockoffs (version 0.9.1)

MFKnockoffs.stat.lasso_coef_difference: Cross-validated penalized linear regression statistics for MFKnockoffs

Description

Fit 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 \(\lambda\) is selected by cross-validation and computed with glmnet.

Usage

MFKnockoffs.stat.lasso_coef_difference(X, X_k, y, cores = 2, ...)

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

cores

Number of cores used to compute the knockoff 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)

Value

A vector of statistics \(W\) (length p)

Details

This function uses the glmnet package to fit the lasso path.

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

The knockoff 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 \(\lambda\)'s. The default value of nlambda is 100, 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': 100).

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

See Also

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_lambda_difference_bin, MFKnockoffs.stat.lasso_lambda_difference, MFKnockoffs.stat.random_forest, MFKnockoffs.stat.sqrt_lasso, MFKnockoffs.stat.stability_selection

Examples

# NOT RUN {
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.lasso_coef_difference)
print(result$selected)

# Advanced usage with custom arguments
foo = MFKnockoffs.stat.lasso_coef_difference
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)

# }