APPLE: Approximate Path for Penalized Likelihood Estimators

TL;DR

The paper introduces APPLE, an efficient algorithm for computing solution paths of penalized likelihood estimators, applicable to both convex and nonconvex penalties, improving variable selection and estimation in high-dimensional data.

Contribution

APPLE is a novel hybrid algorithm combining predictor-corrector and coordinate descent methods for high-dimensional penalized likelihood estimation.

Findings

APPLE outperforms existing methods in simulations.

APPLE effectively handles both convex and nonconvex penalties.

Application to gene expression data demonstrates practical utility.

Abstract

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonconvex penalty (such as SCAD and MCP) cases are considered. The APPLE efficiently computes the solution path for the penalized likelihood estimator using a hybrid of the modified predictor-corrector method and the coordinate-descent algorithm. APPLE is compared with several well-known packages via simulation and analysis of two gene expression data sets.