Bayesian Hierarchical Stacking: Some Models Are (Somewhere) Useful*

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can further improve the stacked mixture with a hierarchical model. We generalize stacking to Bayesian hierarchical stacking. The model weights are varying as a function of data, partially-pooled, and inferred using Bayesian inference. We further incorporate discrete and continuous inputs, other structured priors, and time series and longitudinal data. To verify the performance gain of the proposed method, we derive theory bounds, and demonstrate on several applied problems.

Automated summary

This article introduces a model averaging technique called Stacking, which achieves optimal predictions through linear averaging of different models. The article also proposes an improvement method using a hierarchical model and extends Stacking to Bayesian hierarchical stacking. Experimental results demonstrate that this method can achieve better performance on different types of data.