An overview of reciprocal L 1 ‐regularization for high dimensional regression data

High dimensional data plays a key role in the modern statistical analysis. A common objective for the high dimensional data analysis is to perform model selection, and penalized likelihood method is one of the most popular approaches. Typical penalty functions are usually symmetric about 0, continuous and nondecreasing in (0, ∞). In this review article, we will focus on a special type of penalty function, the so call reciprocal Lasso ( rLasso ) penalty. The rLasso penalty functions are decreasing in (0, ∞), discontinuous at 0, and converge to infinity when the coefficients approach zero. Although uncommon, this choice of penalty is intuitively appealing if one seeks a parsimonious model fitting. In this article, we will provide an overview for the motivation, theory, and computational challenges of this rLasso penalty, and we will also compare the theoretical properties and empirical performance of rLasso with other popular penalty choices. WIREs Comput Stat 2018, 10:e1416. doi: 10.1002/wics.1416 This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods