Search results for "Identifiability condition"

On the sign recovery by LASSO, thresholded LASSO and thresholded Basis Pursuit Denoising

2020

Basis Pursuit (BP), Basis Pursuit DeNoising (BPDN), and LASSO are popular methods for identifyingimportant predictors in the high-dimensional linear regression model Y = Xβ + ε. By definition, whenε = 0, BP uniquely recovers β when Xβ = Xb and β different than b implies L1 norm of β is smaller than the L1 norm of b (identifiability condition). Furthermore, LASSO can recover the sign of β only under a much stronger irrepresentability condition. Meanwhile, it is known that the model selection properties of LASSO can be improved by hard-thresholdingits estimates. This article supports these findings by proving that thresholded LASSO, thresholded BPDNand thresholded BP recover the sign of β in …