通过多次运行改进贝叶斯推断,提升复杂后验分布的探索精度。
Stacking Variational Bayesian Monte Carlo
- 用多轮独立VBMC构建局部近似,再融合成全局后验
- 在不增加计算量前提下显著改善后验估计质量
- 适合高成本黑箱似然模型,可并行部署
针对计算成本高、不可解析的黑箱似然模型,贝叶斯推断面临巨大挑战,尤其当后验分布复杂时。现有方法在有限似然评估预算下难以高效探索参数空间。变分贝叶斯蒙特卡洛(VBMC)虽样本高效,但其保守探索策略易遗漏后验中的重要区域,如独立模态或长尾部分。本文提出堆叠变分贝叶斯蒙特卡洛(S-VBMC),通过多个独立VBMC运行构建局部近似,并利用其混合后验表示和每组证据估计,以一种理论严谨且低成本的方式融合为全局近似。关键优势在于无需额外似然评估,天然支持并行化,可无缝集成至现有推理流程。在两个设计用于挑战VBMC探索能力的合成问题及两个来自计算神经科学的真实应用中,均展现出显著更优的后验逼近效果。代码已开源:https://github.com/acerbilab/svbmc。
原文摘要 · Abstract (English)
Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter space efficiently under a limited budget of likelihood evaluations. Variational Bayesian Monte Carlo (VBMC) is a sample-efficient method that addresses this by building a local surrogate model of the log-posterior. However, its conservative exploration strategy, while promoting stability, can cause it to miss important regions of the posterior, such as distinct modes or long tails. In this work, we introduce Stacking Variational Bayesian Monte Carlo (S-VBMC), a method that overcomes this limitation by constructing a robust, global posterior approximation from multiple independent VBMC runs. Our approach merges these local approximations through a principled and inexpensive post-processing step that leverages VBMC's mixture posterior representation and per-component evidence estimates. Crucially, S-VBMC requires no additional likelihood evaluations and is naturally parallelisable, fitting seamlessly into existing inference workflows. We demonstrate its effectiveness on two synthetic problems designed to challenge VBMC's exploration and two real-world applications from computational neuroscience, showing substantial improvements in posterior approximation quality across all cases. Our code is available as a Python package at https://github.com/acerbilab/svbmc.
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