mlsanityData to 7 Oct 2026

Bayesian hierarchical stacking: Some models are (somewhere) useful

arXiv 2101.08954 ↗First posted 22 Jan 2021stat.ME cs.LG stat.MLcited by 14

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Abstract (arXiv)

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.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 13 of its 53 references that are in the map. First posted on arXiv 22 Jan 2021.

Builds on

13 of 53 references.

References · 13

  1. 2015Practical Bayesian model evaluation using leave-one-out cross-validation and WAICcited by 110
  2. 2020Bayesian Workflowcited by 47
  3. 2015Pareto Smoothed Importance Samplingcited by 42
  4. 2017Using stacking to average Bayesian predictive distributionscited by 39
  5. 2019Stacking Models for Nearly Optimal Link Prediction in Complex Networkscited by 35
  6. 2020Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriorscited by 29
  7. 2015Comparison of Bayesian predictive methods for model selectioncited by 10
  8. 2019Approximate leave-future-out cross-validation for Bayesian time series modelscited by 10
  9. 2016Improved prediction accuracy for disease risk mapping using Gaussian Process stacked generalisationcited by 8
  10. 2014Minimax Optimal Bayesian Aggregationcited by 2
  11. 2014Testing hypotheses via a mixture estimation modelcited by 2
  12. 2016Reducing the error of Monte Carlo Algorithms by Learning Control Variatescited by 1
1 more
  1. 2019Bayesian Aggregationcited by 1

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Citing papers per year: 2023: 6; 2024: 5; 2025: 1; 2026: 2.

14 papers.

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  1. 2024Amortized Bayesian Multilevel Modelscited by 12
  2. 2024Dynamic Online Ensembles of Basis Expansionscited by 5
  3. 2023Local Bayesian Dirichlet mixing of imperfect modelscited by 2
  4. 2024Fusion of Gaussian Processes Predictions with Monte Carlo Samplingcited by 1
  5. 2024Model orthogonalization and Bayesian forecast mixing via Principal Component Analysiscited by 1
  6. 2023Fitting Low-rank Models on Egocentrically Sampled Partial Networkscited by 0
  7. 2023Locking and Quacking: Stacking Bayesian model predictions by log-pooling and superpositioncited by 0
  8. 2023Automating Model Comparison in Factor Graphscited by 0
  9. 2023On the meaning of uncertainty for ethical AI: philosophy and practicecited by 0
  10. 2023Beyond Bayesian Model Averaging over Paths in Probabilistic Programs with Stochastic Supportcited by 0
  11. 2024BayesBlend: Easy Model Blending using Pseudo-Bayesian Model Averaging, Stacking and Hierarchical Stacking in Pythoncited by 0
  12. 2025Input Adaptive Bayesian Model Averagingcited by 0
2 more
  1. 2026A Divergence-Based Method for Weighting and Averaging Model Predictionscited by 0
  2. 2026A renormalization-group inspired lattice-based framework for piecewise generalized linear modelscited by 0