用变分推断与归一化流训练可逆跳跃提议，提升跨模型贝叶斯推断效率。
A Novel Framework Using Variational Inference with Normalizing Flows to Train Transport Reversible Jump Proposals
- 结合变分推断与条件归一化流，优化跨模型与模型内提议。
- 相比已有方法，计算成本更低且混合速度更快，提升采样效率。
- 适合需要高效模型比较与高维参数推断的研究者使用。
我们提出一种统一框架，利用变分推断（VI）结合（条件）归一化流（NFs）训练可逆跳马尔可夫链蒙特卡洛中的跨模型与模型内提议，实现高效的跨维度贝叶斯推断。与Davies等（2023）的传输可逆跳跃（TRJ）方法不同，该框架最小化反向KL散度，仅需来自简单基分布的样本，显著降低计算成本。特别地，我们提出一种新型跨维度变分推断方法，使用条件归一化流拟合Davies等（2023）的条件传输提议。采用RealNVP流学习模型特定的传输映射，使计算可并行化。本框架还可提供精确的边际似然估计，有助于高效模型比较并设计无拒绝提议。大量数值实验表明，基于该框架训练的TRJ方法在混合速度上优于现有基线。
原文摘要 · Abstract (English)
We propose a unified framework that employs variational inference (VI) with (conditional) normalizing flows (NFs) to train both between-model and within-model proposals for reversible jump Markov chain Monte Carlo, enabling efficient trans-dimensional Bayesian inference. In contrast to the transport reversible jump (TRJ) of Davies et al. (2023), which optimizes forward KL divergence using pilot samples from the complex target distribution, our approach minimizes the reverse KL divergence, requiring only samples from a simple base distribution and largely reducing computational cost. Especially, we develop a novel trans-dimensional VI method with conditional NFs to fit the conditional transport proposal of Davies et al. (2023). We use RealNVP flows to learn the model-specific transport maps used for constructing proposals so that the calculation is parallelizable. Our framework also provides accurate estimates of marginal likelihoods, which may facilitate efficient model comparison and help design rejection-free proposals. Extensive numerical studies demonstrate that the TRJ method trained under our framework achieves faster mixing compared to existing baselines.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。