This function samples second-order multivariate Gaussian knockoff variables. First, a multivariate Gaussian distribution is fitted to the observations of X. Then, Gaussian knockoffs are generated according to the estimated model.
create.second_order(X, method = c("asdp", "equi", "sdp"), shrink = F)
n-by-p matrix of original variables.
either "equi", "sdp" or "asdp" (default: "asdp"). This determines the method that will be used to minimize the correlation between the original variables and the knockoffs.
whether to shrink the estimated covariance matrix (default: F).
If the argument
shrink is set to T, a James-Stein-type shrinkage estimator for
the covariance matrix is used instead of the traditional maximum-likelihood estimate. This option
requires the package
cov.shrink for more details.
Even if the argument
shrink is set to F, in the case that the estimated covariance
matrix is not positive-definite, this function will apply some shrinkage.
A n-by-p matrix of knockoff variables.
Candes et al., Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection, arXiv:1610.02351 (2016). https://web.stanford.edu/group/candes/knockoffs/index.html
set.seed(2022) p=100; n=80; k=15 rho = 0.4 Sigma = toeplitz(rho^(0:(p-1))) X = matrix(rnorm(n*p),n) %*% chol(Sigma) nonzero = sample(p, k) beta = 3.5 * (1:p %in% nonzero) y = X %*% beta + rnorm(n) # Basic usage with default arguments result = knockoff.filter(X, y, knockoffs=create.second_order) print(result$selected) # Advanced usage with custom arguments knockoffs = function(X) create.second_order(X, method='equi') result = knockoff.filter(X, y, knockoffs=knockoffs) print(result$selected)
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