arXiv：cs.LG（机器学习，全量分类）· Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian Wang·· 9 小时前AI 评分30
基于先验少步传输映射的源空间 MCMC 后验采样
Posterior sampling by source-space MCMC via prior-based few-step transport maps
AI 导读
研究者提出源空间广义贝叶斯推断框架，用一步或少步改进 MeanFlow（iMF）映射表示隐式先验，并在其高斯源空间中完成后验采样。该方法给出了精确后验与学习后验之间的 Wasserstein 误差界，并采用带预条件 Crank-Nicolson 更新的并行回火及融合分裂 Hamiltonian Monte Carlo 的混合变体提升采样效率。
正文
Abstract:Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models. The same computational problem appears in the test-time guidance task (generalized Bayes), where an explicit positive weight, e.g., an exponentiated reward, tilts an implicit prior. We develop a framework for source-space generalized Bayesian inference that combines inexpensive few-step prior transports with posterior stability guarantees. Specifically, we represent the prior using a one- or few-step improved MeanFlow (iMF) map and perform posterior sampling in its Gaussian source space. We establish Wasserstein error bounds between the exact and learned posteriors in terms of the joint population iMF and auxiliary-velocity loss, decomposed into training suboptimality and model-class approximation error. In the iMF source space, we adopt parallel tempering with preconditioned Crank-Nicolson updates and introduce a hybrid variant that incorporates split Hamiltonian Monte Carlo to improve sampling efficiency. Synthetic experiments show that the proposed framework can approximate posterior distributions accurately and efficiently, while CLIP-guided ImageNet experiments demonstrate its ability to steer a pretrained iMF image prior toward text-specified preferences.
| Subjects: | Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.01034 [stat.ML] |
| (or arXiv:2610.01034v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01034 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Hoang Phuc Hau Luu [view email]
[v1]
Thu, 1 Oct 2026 04:21:08 UTC (17,484 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org