摊销变分跨维度推理 (Amortized variational transdimensional inference)

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has expanded the application of optimization-based Bayesian inference to highly complex problems. However, despite the importance of multi-model Bayesian inference, defined over a transdimensional joint model and parameter space, flow-based SVI has been limited to problems defined over a fixed-dimensional parameter space. We introduce CoSMIC normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables use of a single amortized variational density for inference over a transdimensional (multi-model) conditional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using ideas from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments show the performance of VTI on challenging problems that scale to high-cardinality model spaces.

翻译：基于流的模型表达能力与随机变分推理（SVI）的结合，已将基于优化的贝叶斯推理应用扩展至高度复杂的问题。然而，尽管跨维度联合模型与参数空间的多模型贝叶斯推理具有重要意义，基于流的SVI此前仍局限于固定维度参数空间的问题。我们提出了CoSMIC归一化流（上下文指定掩码的恒等映射组件），这是对神经自回归条件归一化流架构的扩展，使得单个摊销变分密度能够用于跨维度（多模型）条件目标分布的推理。我们提出了一种结合随机变分跨维度推理（VTI）的方法，利用贝叶斯优化和蒙特卡洛梯度估计的思想训练CoSMIC流。数值实验展示了VTI在具有挑战性问题上的性能，这些问题可扩展至高基数模型空间。