Bayesian Hierarchical Stacking: Some Models Are (Somewhere) Useful

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-12
Major/Subject
Mcode
Degree programme
Language
en
Pages
29
1043-1071
Series
Bayesian Analysis, Volume 17, issue 4
Abstract
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.
Description
Publisher Copyright: © 2022 International Society for Bayesian Analysis
Keywords
Bayesian hierarchical modeling, Conditional prediction, Covariate shift, Model averaging, Prior construction, Stacking
Other note
Citation
Yao, Y, Pirš, G, Vehtari, A & Gelman, A 2022, ' Bayesian Hierarchical Stacking: Some Models Are (Somewhere) Useful ', Bayesian Analysis, vol. 17, no. 4, pp. 1043-1071 . https://doi.org/10.1214/21-BA1287