Ranked Sparsity: A Cogent Regularization Framework for Selecting and Estimating Feature Interactions and Polynomials

TL;DR

This paper introduces ranked sparsity, a regularization framework that improves feature interaction selection by requiring stronger evidence for inclusion, leading to more accurate, interpretable, and less overfitted models.

Contribution

It proposes the sparsity-ranked lasso (SRL) method that addresses covariate equipoise and enhances model selection for interactions and polynomials.

Findings

SRL outperforms competing methods in simulations

SRL produces more transparent models with fewer false interactions

SRL is fast and accurate in high-dimensional settings

Abstract

We explore and illustrate the concept of ranked sparsity, a phenomenon that often occurs naturally in modeling applications when an expected disparity exists in the quality of information between different feature sets. Its presence can cause traditional and modern model selection methods to fail because such procedures commonly presume that each potential parameter is equally worthy of entering into the final model - we call this presumption "covariate equipoise". However, this presumption does not always hold, especially in the presence of derived variables. For instance, when all possible interactions are considered as candidate predictors, the premise of covariate equipoise will often produce over-specified and opaque models. The sheer number of additional candidate variables grossly inflates the number of false discoveries in the interactions, resulting in unnecessarily complex and difficult-to-interpret models with many (truly spurious) interactions. We suggest a modeling strategy that requires a stronger level of evidence in order to allow certain variables (e.g. interactions) to be selected in the final model. This ranked sparsity paradigm can be implemented with the sparsity-ranked lasso (SRL). We compare the performance of SRL relative to competing methods in a series of simulation studies, showing that the SRL is a very attractive method because it is fast, accurate, and produces more transparent models (with fewer false interactions). We illustrate its utility in an application to predict the survival of lung cancer patients using a set of gene expression measurements and clinical covariates, searching in particular for gene-environment interactions.