用流匹配模型提升复杂多峰后验的边缘似然估计精度
Learned harmonic mean estimation of the marginal likelihood for multimodal posteriors with flow matching
- 基于流匹配构建连续归一化流，用于优化边缘似然估计中的密度估计
- 在20维参数空间的多峰后验上实现稳定估计，无需调参或修改基分布
- 适用于任意采样方法，适合需要精确模型比较的复杂贝叶斯建模场景
边缘似然（即贝叶斯证据）是贝叶斯模型比较的关键量，但对复杂模型尤其在中等维度参数空间中计算困难。已有研究证明，学习型调和均值估计器仅需后验样本即可提供准确且鲁棒的边缘似然估计，且对采样策略无依赖，可与任意采样方法结合使用。然而，先前用于该估计的内部密度估计器在高度多峰后验中表现不佳。本文引入基于流匹配的连续归一化流作为内部密度估计的强大架构，显著提升了对复杂多峰后验的处理能力。我们在一个20参数维度的挑战性例子中展示了该方法的有效性，证明其无需精细调参或对基分布进行启发式修改即可处理复杂后验。
原文摘要 · Abstract (English)
The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean estimator has been shown to provide accurate and robust estimates of the marginal likelihood simply using posterior samples. It is agnostic to the sampling strategy, meaning that the samples can be obtained using any method. This enables marginal likelihood calculation and model comparison with whatever sampling is most suitable for the task. However, the internal density estimators considered previously for the learned harmonic mean can struggle with highly multimodal posteriors. In this work we introduce flow matching-based continuous normalizing flows as a powerful architecture for the internal density estimation of the learned harmonic mean. We demonstrate the ability to handle challenging multimodal posteriors, including an example in 20 parameter dimensions, showcasing the method's ability to handle complex posteriors without the need for fine-tuning or heuristic modifications to the base distribution.
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