将模型先验融入流模型，提升复杂贝叶斯后验逼近效果。
Model-Informed Flows for Bayesian Inference
- 基于理论证明，将VIP与全秩高斯结合可表示为带平移的前向自回归流。
- 在多类层次与非层次模型上，后验逼近更紧致，性能达或超越当前最优。
- 适合需高精度后验推断的复杂贝叶斯建模场景，如医疗、金融领域。
变分推断在处理复杂层次化贝叶斯模型的后验几何时常遇困难。近期的基于流的变分族与变分推断参数（VIP）分别应对了部分挑战，但二者间的理论关联未被探索。本文证明，将VIP与全秩高斯结合可精确表示为带有平移项和模型先验输入的前向自回归流。基于此理论洞察，我们提出模型引导流（Model-Informed Flow, MIF）架构，引入必要平移机制、先验信息及层次排序。实验表明，MIF在一系列层次与非层次基准测试中均实现更紧致的后验近似，性能达到或超过当前最先进水平。
原文摘要 · Abstract (English)
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.
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