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Cross-study replicability is a powerful model evaluation criterion thatemphasizes generalizability of predictions. When training cross-studyreplicable prediction models, it is critical to decide between merging andtreating the studies separately. We study boosting algorithms in the presenceof potential heterogeneity in predictor-outcome relationships across studiesand compare two multi-study learning strategies: 1) merging all the studies andtraining a single model, and 2) multi-study ensembling, which involves traininga separate model on each study and ensembling the resulting predictions. In theregression setting, we provide theoretical guidelines based on an analyticaltransition point to determine whether it is more beneficial to merge or toensemble for boosting with linear learners. In addition, we characterize abias-variance decomposition of estimation error for boosting withcomponent-wise linear learners. We verify the theoretical transition pointresult in simulation and illustrate how it can guide the decision on mergingvs. ensembling in an application to breast cancer gene expression data.

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