Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure
Abstract
We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a directed acyclic graph, our method automatically derives valid factorizations of the joint posterior and matching neural network architectures. The key steps, graph expansion and graph inversion, yield an inverse graph that determines how inference networks are stacked and conditioned, producing factorizations that amortize over the number of groups and the number of observations within each group. Unlike approaches that simplify the dependency structure to speed up learning or inference, our method preserves all conditional independence and exchangeability assumptions of the generative model. Across three case studies, it closely matches gold-standard samplers on models with more than 6,500 parameters while reducing inference to a near-instant forward pass once trained.
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BibTeX
@misc{habermann2026amortized,
title = {{Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure}},
author = {Daniel Habermann and Andreas Bulling and Stefan T. Radev and Paul-Christian Bürkner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40024},
eprint = {2609.40024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40024},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure
AU - Daniel Habermann
AU - Andreas Bulling
AU - Stefan T. Radev
AU - Paul-Christian Bürkner
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40024
UR - https://arxiv.org/abs/2609.40024
AB - We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a directed acyclic graph, our method automatically derives valid factorizations of the joint posterior and matching neural network architectures. The key steps, graph expansion and graph inversion, yield an inverse graph that determines how inference networks are stacked and conditioned, producing factorizations that amortize over the number of groups and the number of observations within each group. Unlike approaches that simplify the dependency structure to speed up learning or inference, our method preserves all conditional independence and exchangeability assumptions of the generative model. Across three case studies, it closely matches gold-standard samplers on models with more than 6,500 parameters while reducing inference to a near-instant forward pass once trained.
ER -