MFKnockoffs package can also be used to perform controlled variable selection with a fixed design matrix, assuming a linear regression model for the response. In this sense,
MFKnockoffs is a superset of the original knockoffs package.
# Problem parameters n = 1000 # number of observations p = 300 # number of variables k = 30 # number of variables with nonzero coefficients amplitude = 4.5 # signal amplitude (for noise level = 1) # Generate the variables from a multivariate normal distribution mu = rep(0,p); Sigma = diag(p) X = matrix(rnorm(n*p),n) # Generate the response from a linear model nonzero = sample(p, k) beta = amplitude * (1:p %in% nonzero) / sqrt(n) y.sample = function(X) X %*% beta + rnorm(n) y = y.sample(X)
In order to create fixed-design knockoffs, we call
MFKnockoffs.filter with the parameter
statistic equal to
MFKnockoffs.stat.glmnet_lambda_difference. Moreover, since not all statistics are valid with fixed-design knockoffs, we use
MFKnockoffs.stat.glmnet_lambda_difference instead of the default one (which is based on cross-validation).
library(MFKnockoffs) result = MFKnockoffs.filter(X, y, knockoffs = MFKnockoffs.create.fixed, statistic = MFKnockoffs.stat.glmnet_lambda_difference)
We can display the results with
The default value for the target false discovery rate is 0.1. In this experiment the false discovery proportion is
fdp = function(selected) sum(beta[selected] == 0) / max(1, length(selected)) fdp(result$selected)
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