基于流匹配的连续归一化流用于多模后验的学得谐均估计
Learned harmonic mean estimation of the marginal likelihood for multimodal posteriors with flow matching
AI总结：
本文提出基于流匹配的连续归一化流，用于高效估计多模后验的边际似然，解决了传统方法在处理复杂后验时的局限性。
摘要：
边际似然，或贝叶斯证据，是贝叶斯模型比较中的关键量，但其计算对于复杂模型甚至在中等维度参数空间中也具有挑战性。已学习的谐均估计器已被证明可以仅使用后验样本就提供准确且稳健的边际似然估计。它不依赖于采样策略，意味着样本可以使用任何方法获得。这使边际似然计算和模型比较能够使用最适合任务的采样方法。然而，之前考虑的用于已学习谐均的内部密度估计器在处理高度多模后验时可能会遇到困难。在本工作中，我们引入了基于流匹配的连续归一化流作为已学习谐均内部密度估计的强大架构。我们展示了处理具有挑战性的多模后验的能力，包括一个20参数维度的例子，展示了该方法在无需对基础分布进行微调或启发式修改的情况下处理复杂后验的能力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
