Model-Informed Flows for Bayesian Inference
This addresses the problem of improving Bayesian inference accuracy for researchers and practitioners, though it appears incremental as it builds on existing methods like VIP and flow-based families.
The paper tackled the challenge of variational inference struggling with posterior geometry in complex hierarchical Bayesian models by introducing the Model-Informed Flow (MIF) architecture, which delivered tighter posterior approximations and matched or exceeded state-of-the-art performance across benchmarks.
Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow-based variational families and Variationally Inferred Parameters (VIP) each address aspects of this challenge, but their formal relationship is unexplored. Here, we prove that the combination of VIP and a full-rank Gaussian can be represented exactly as a forward autoregressive flow augmented with a translation term and input from the model's prior. Guided by this theoretical insight, we introduce the Model-Informed Flow (MIF) architecture, which adds the necessary translation mechanism, prior information, and hierarchical ordering. Empirically, MIF delivers tighter posterior approximations and matches or exceeds state-of-the-art performance across a suite of hierarchical and non-hierarchical benchmarks.