Learning interactions through hierarchical group-lasso regularization

TL;DR

This paper presents a hierarchical group-lasso regularization method for learning pairwise interactions that ensures interpretability and strong hierarchy, applicable to categorical, continuous, and mixed variables, demonstrated on simulated and real data.

Contribution

The paper introduces a novel hierarchical group-lasso approach for interaction learning that simplifies model constraints and enhances interpretability across variable types.

Findings

Effective in modeling interactions for categorical and continuous variables

Outperforms existing methods on simulated data

Successfully applied to genome-wide association study data

Abstract

We introduce a method for learning pairwise interactions in a manner that satisfies strong hierarchy: whenever an interaction is estimated to be nonzero, both its associated main effects are also included in the model. We motivate our approach by modeling pairwise interactions for categorical variables with arbitrary numbers of levels, and then show how we can accommodate continuous variables and mixtures thereof. Our approach allows us to dispense with explicitly applying constraints on the main effects and interactions for identifiability, which results in interpretable interaction models. We compare our method with existing approaches on both simulated and real data, including a genome wide association study, all using our R package glinternet.