Split Knockoffs for Structural Sparsity
singular value decomposition
calculate the CV optimal beta
calculate the CV optimal beta and estimated support set
hitting point calculator on a given path
default normalization function for matrix
split knockoff selector given W statistics
generate split knockoff copies
make SVD as well as orthogonal complements
split Knockoff filter for structural sparsity problem
W statistics generator based on a fixed beta(lambda) = hat beta
W statistics generator based on the beta(lambda) from a split LASSO pa...
compute the threshold for variable selection
Split Knockoff is a data adaptive variable selection framework for controlling the (directional) false discovery rate (FDR) in structural sparsity, where variable selection on linear transformation of parameters is of concern. This proposed scheme relaxes the linear subspace constraint to its neighborhood, often known as variable splitting in optimization. Simulation experiments can be reproduced following the Vignette. 'Split Knockoffs' is first defined in Cao et al. (2021) <doi:10.48550/arXiv.2103.16159>.