Numerical characterization of support recovery in sparse regression with correlated design

Sparse regression is employed in diverse scientific settings as a feature selection method. A pervasive aspect of data the presence correlations between predictive features. These hamper both and estimation jeopardize conclusions drawn from estimated models. On other hand, theoretical results on sparsity-inducing regularized have largely addressed conditions for consistency via asymptotics, disregard problem model selection, whereby regularization parameters are chosen. In this numerical study, we address these issues through exhaustive characterization performance several estimators, coupled with range strategies. estimators criteria were examined across correlated problems varying degrees signal to noise, distributions non-zero coefficients, sparsity. Our reveal fundamental tradeoff false positive negative control all examined. Additionally, numerically explore transition point modulated by signal-to-noise ratio spectral properties design covariance matrix at which accuracy considered algorithms degrades. Overall, find that SCAD BIC or empirical Bayes performs best considered.