Compositional Amortized Inference for Large-Scale Hierarchical Bayesian Models
Abstract
Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, has been a major hurdle due to the need to simulate and process massive datasets. Our study tackles these challenges by extending compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. We develop a new error-damping estimator to address previous stability issues of CSM when aggregating large numbers of data points. We first verified the numerical stability with up to 100,000 data points on a controlled benchmark. We then evaluated our method on a hierarchical AR model, achieving competitive performance to direct ABI baselines on smaller problem sizes while using less than one full model simulation for larger problem sizes. Finally, we address a large-scale inverse problem in advanced microscopy with over 750,000 parameters, demonstrating its relevance to real scientific applications.
Cite
Text
Arruda et al. "Compositional Amortized Inference for Large-Scale Hierarchical Bayesian Models." International Conference on Learning Representations, 2026.Markdown
[Arruda et al. "Compositional Amortized Inference for Large-Scale Hierarchical Bayesian Models." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/arruda2026iclr-compositional/)BibTeX
@inproceedings{arruda2026iclr-compositional,
title = {{Compositional Amortized Inference for Large-Scale Hierarchical Bayesian Models}},
author = {Arruda, Jonas and Pandey, Vikas and Sherry, Catherine and Barroso, Margarida and Intes, Xavier and Hasenauer, Jan and Radev, Stefan T.},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/arruda2026iclr-compositional/}
}