用流模型回归已有似然数据，实现高效贝叶斯推断
Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations
- 通过回归已有对数密度值直接构建可计算后验
- 在神经科学与生物应用中表现优于或媲美现有方法
- 适合似然函数计算昂贵、已有模型评估可复用的场景
在诸多科学领域，计算成本高昂的似然评估使得贝叶斯推断仍面临重大挑战。我们提出归一化流回归（NFR），一种新型离线推断方法，用于近似后验分布。与传统代理方法需额外采样或推断步骤不同，NFR通过在已有对数密度评估上进行回归，直接生成可处理的后验近似。我们引入专为流回归设计的训练技巧，如定制先验和似然函数，以实现稳健的后验与模型证据估计。我们在合成基准及神经科学与生物学的真实应用场景中验证了NFR的有效性，其性能优于或媲美现有方法。当标准方法计算代价过高，或已有模型评估可复用时，NFR是一种有前景的贝叶斯推断方案。
原文摘要 · Abstract (English)
Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior distributions. Unlike traditional surrogate approaches that require additional sampling or inference steps, NFR directly yields a tractable posterior approximation through regression on existing log-density evaluations. We introduce training techniques specifically for flow regression, such as tailored priors and likelihood functions, to achieve robust posterior and model evidence estimation. We demonstrate NFR's effectiveness on synthetic benchmarks and real-world applications from neuroscience and biology, showing superior or comparable performance to existing methods. NFR represents a promising approach for Bayesian inference when standard methods are computationally prohibitive or existing model evaluations can be recycled.
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