用加权流模型高效推断多模态后验，避免采样训练。
Amortized Inference of Multi-Modal Posteriors using Likelihood-Weighted Normalizing Flows
- 基于似然加权重要性采样训练归一化流，实现参数高效推断。
- 标准单峰基分布会错误连接不连通模式，产生虚假概率桥。
- 初始化为匹配目标模态数的高斯混合模型，显著提升重构精度。
我们提出一种新型变分后验估计方法，采用似然加权重要性采样训练归一化流，可在无需后验采样样本的情况下，高效求解高维逆问题中的理论参数。在二维与三维多模态基准任务中验证了该方法的有效性。研究发现，基分布的拓扑结构对建模后验影响显著：标准单峰基分布无法捕捉不连通支撑集，导致模式间出现虚假概率连接。我们证明，若将流模型初始化为与目标模态数量一致的高斯混合模型，可显著提升重构保真度（通过距离与散度指标衡量）。最后，将该方法应用于重夸克物理中的具体问题——从 $B^0\to J/ψ\,K^0$ 的CP不对称性中提取Wolfenstein参数，该问题具有多模态、非高斯及模式权重不对称特征，并与收敛良好的马尔可夫链蒙特卡洛参考结果进行多维度对比。
原文摘要 · Abstract (English)
We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional inverse problems without the need for posterior training samples. We implement the method on multi-modal benchmark tasks in 2D and 3D to check for the efficacy. A critical observation of our study is the impact of the topology of the base distributions on the modelled posteriors. We find that standard unimodal base distributions fail to capture disconnected support, resulting in spurious probability \textit{bridges} between modes. We demonstrate that initializing the flow with a Gaussian Mixture Model that matches the cardinality of the target modes significantly improves reconstruction fidelity, as measured by some distance and divergence metrics. Finally, we apply this method to a curated problem in heavy flavour physics --- the extraction of the Wolfenstein parameters from the CP asymmetry in $B^0\to J/ψ\,K^0$; it is multimodal, non-Gaussian, and asymmetric in its mode weights --- and compare the results against a well-converged Markov Chain Monte Carlo reference using different metrics.
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