A Model Selection Criterion for LASSO Estimate with Scaling

Katsuyuki Hagiwara

Abstract: There have been several studies to relax a bias problem in LASSO (Least Absolute Shrinkage and Selection Operator). In this article, we considered to solve a bias problem of LASSO estimator by scaling and derived a model selection criterion under the scaling method. The proposed scaling value is valid to compensate the excessive shrinkage of LASSO estimator and is easy to compute by using LASSO estimator. Moreover, we derived SURE (Stein’s Unbiased Risk Estimate) as a model selection criterion. This analytic solution is also a benefit of the proposed scaling value. Furthermore, we verified the risk estimate and confirmed its effectiveness through a simple numerical example.