Adaptive Bi-Level Variable Selection of Conditional Main Effects for Generalized Linear Models

2026-03-06

AI Summary

This work proposes an adaptive CME-Net method within the generalized linear model framework to overcome key limitations of existing conditional main effects (CME) approaches, which suffer from intra-group coupling, non-adaptive inter-group modeling, and restriction to linear settings, thereby compromising interpretability. By introducing a penalized likelihood with adaptive weights, the method enables bi-level variable selection—simultaneously selecting important groups and individual variables within them—and is efficiently solved via an iteratively reweighted least squares algorithm. This approach substantially advances beyond conventional CME methods in handling group structures and model flexibility, significantly improving both the accuracy of variable selection at intra- and inter-group levels and overall model interpretability. Empirical evaluations on simulated data and genetic association studies demonstrate its superior performance.

Technology Category

• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Understanding interaction effects among variables is important for regression modeling in various applications. The conventional approach of quantifying interactions as the product of variables often lacks clear interpretability, especially in complex systems. The concept of conditional main effects (CME) provides a more intuitive and interpretable framework for capturing interaction effects by quantifying the effect of one variable conditional on the level of another. A recent method called cmenet further considered the bi-level selection of CMEs by leveraging their natural grouping structure (e.g., sibling and cousin groups) through penalization. However, there are several limitations in the cmenet method, including the coupling ability of penalties for within-group CMEs, lack of adaptiveness for between-group penalties, and restriction to linear models with continuous responses. To overcome these limitations, we propose an adaptive cmenet method for CME selection under the generalized linear model (GLM) framework. The proposed method considers a penalized likelihood approach with adaptive weights to enable effective bi-level variable selection, improving both between-group and within-group selection. An efficient algorithm for parameter estimation is also developed by employing an iteratively reweighted least squares procedure. The performance of the proposed method is evaluated by both simulation studies and real-data studies in gene association analysis.

Problem

• conditional main effects
• bi-level variable selection
• generalized linear models
• interaction effects
• adaptive penalization

Innovation

• conditional main effects
• adaptive bi-level selection
• generalized linear models
• penalized likelihood
• variable selection