Variable Selection via Subtle Uprooting
This article proposes a variable selection method termed “subtle uprooting” for linear regression. In this proposal, variable selection is formulated into a single optimization problem by approximating cardinality involved in the information criterion with a smooth function. A technical maneuver is then employed to enforce sparsity of parameter estimates while maintaining smoothness of the objective function. To solve the resulting smooth nonconvex optimization problem, a modified Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with established global and super-linear convergence is adopted. Both simulated experiments and an empirical example are provided for assessment and illustration. Supplementary materials for this article are available online.