无需似然评估，用流匹配快速生成贝叶斯后验采样
Conditional Flow Matching for Bayesian Posterior Inference
- 在数据与参数联合空间构建动态块三角速度场，实现确定性映射
- 可逆积分得向量秩，支持高效生成贝叶斯可信集，轮廓对应深度等高线
- 计算轻量，适合作为复杂后验结构的快速推断工具
我们提出一种基于流匹配的多元后验采样方法。该方法具有简洁的训练目标，无需访问似然函数评估。通过在数据与参数的联合空间中学习一个动态、块三角速度场，实现从源分布到目标后验的确定性传输映射。其逆映射（称为向量秩）可通过时间可逆积分获得。利用动态设计的优势：对速度施加适当约束可得单调映射，从而构成条件Brenier映射，实现贝叶斯可信集的快速同步生成，其轮廓对应Monge-Kantorovich数据深度的等高线。相比基于GAN和扩散模型的方法，本方法计算更轻量，能有效捕捉复杂后验结构。最后，提供了恢复后验分布及相应贝叶斯可信集一致性的频数理论保证。
原文摘要 · Abstract (English)
We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint space of data and parameters, which results in a deterministic transport map from a source distribution to the desired posterior. The inverse map, named vector rank, is accessible by reversibly integrating the velocity over time. It is advantageous to leverage the dynamic design: proper constraints on the velocity yield a monotone map, which leads to a conditional Brenier map, enabling a fast and simultaneous generation of Bayesian credible sets whose contours correspond to level sets of Monge-Kantorovich data depth. Our approach is computationally lighter compared to GAN-based and diffusion-based counterparts, and is capable of capturing complex posterior structures. Finally, frequentist theoretical guarantee on the consistency of the recovered posterior distribution, and of the corresponding Bayesian credible sets, is provided.
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