Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure

2026-09-30

AI Summary

This study addresses the computational expense and poor scalability of Bayesian inference in multi-layer generative models with arbitrary structures. To overcome this, it proposes an automated derivation framework based on graph unrolling and inversion that exactly factorizes the posterior and yields corresponding neural network architectures without simplifying dependency structures, thereby enabling amortized variational inference while preserving full dependencies. This approach automatically adapts to any directed acyclic graph generative model, rigorously maintaining conditional independence and exchangeability assumptions. Evaluated on models exceeding 6,500 parameters, the method achieves inference accuracy comparable to standard samplers, while post-training inference accelerates to near real-time forward propagation speeds.

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.

Problem

• Amortized Bayesian Inference
• Multilevel Models
• Directed Acyclic Graph
• Posterior Factorization

Innovation

• Amortized Bayesian Inference
• Multilevel Models
• Directed Acyclic Graph
• Graph Inversion
• Neural Network Architecture