Multi-Study Boosting: Theoretical Considerations for Merging vs. Ensembling

TL;DR

This paper explores the theoretical and practical considerations of merging versus ensembling in multi-study boosting, providing guidelines based on heterogeneity and bias-variance trade-offs for better model generalizability.

Contribution

It introduces a theoretical transition point for choosing between merging and ensembling in boosting with linear learners, supported by simulations and real data application.

Findings

Theoretical transition point guides merging vs. ensembling decisions.

Bias-variance analysis clarifies error components in boosting.

Simulation and breast cancer data validate the guidelines.

Abstract

Cross-study replicability is a powerful model evaluation criterion that emphasizes generalizability of predictions. When training cross-study replicable prediction models, it is critical to decide between merging and treating the studies separately. We study boosting algorithms in the presence of potential heterogeneity in predictor-outcome relationships across studies and compare two multi-study learning strategies: 1) merging all the studies and training a single model, and 2) multi-study ensembling, which involves training a separate model on each study and ensembling the resulting predictions. In the regression setting, we provide theoretical guidelines based on an analytical transition point to determine whether it is more beneficial to merge or to ensemble for boosting with linear learners. In addition, we characterize a bias-variance decomposition of estimation error for boosting with component-wise linear learners. We verify the theoretical transition point result in simulation and illustrate how it can guide the decision on merging vs. ensembling in an application to breast cancer gene expression data.