提出新型生成模型，更好捕捉复杂后验的多峰与重尾特征。
Stick-Breaking Mixture Normalizing Flows with Component-Wise Tail Adaptation for Variational Inference
- 用分段混合基替代传统高斯基，缓解反KL散度的模式缺失问题。
- 通过局部尾指数估计与组件定制化变换，实现精准尾部建模。
- 适合需要精确后验推断的复杂数据场景，如高维贝叶斯建模。
基于高斯基的归一化流可高效近似贝叶斯推断中的后验分布，但难以处理具有多峰性与重尾特性的复杂后验。本文提出一种分段混合基结合组件级尾部自适应（StiCTAF）方法：首先学习灵活的混合基，通过各组件ELBO加权平均缓解反KL散度的模式寻求偏差；随后估计未归一化密度的局部尾指数；最后利用共享主干网络结合由尾指数校准的组件特异性尾部变换，对每个混合成分进行精细化调整。该设计在保持精确密度评估与稳定优化的同时，实现准确的模式覆盖与各向异性的尾部建模。在合成后验上的实验表明，该方法在尾部恢复与多模式覆盖方面优于基准模型。真实数据分析进一步展示了其在后验推断中的实际优势。
原文摘要 · Abstract (English)
Normalizing flows with a Gaussian base provide a computationally efficient way to approximate posterior distributions in Bayesian inference, but they often struggle to capture complex posteriors with multimodality and heavy tails. We propose a stick-breaking mixture base with component-wise tail adaptation (StiCTAF) for posterior approximation. The method first learns a flexible mixture base to mitigate the mode-seeking bias of reverse KL divergence through a weighted average of component-wise ELBOs. It then estimates local tail indices of unnormalized densities and finally refines each mixture component using a shared backbone combined with component-specific tail transforms calibrated by the estimated indices. This design enables accurate mode coverage and anisotropic tail modeling while retaining exact density evaluation and stable optimization. Experiments on synthetic posteriors demonstrate improved tail recovery and better coverage of multiple modes compared to benchmark models. We also present a real-data analysis illustrating the practical benefits of our approach for posterior inference.
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