Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is composed of a functional MRI signal measured on 64 thousand brain locations, across 4 measurement sessions, and at least tens of subjects. Even a reduced example on a specific cortical region of 300 brain locations features around 1 million parameters, hampering the usage of modern density estimation techniques such as Simulation-Based Inference (SBI). To infer parameter posterior distributions in this challenging class of problems, we designed a novel methodology that automatically produces a variational family dual to a target HBM. This variatonal family, represented as a neural network, consists in the combination of an attention-based hierarchical encoder feeding summary statistics to a set of normalizing flows. Our automatically-derived neural network exploits exchangeability in the plate-enriched HBM and factorizes its parameter space. The resulting architecture reduces by orders of magnitude its parameterization with respect to that of a typical SBI representation, while maintaining expressivity. Our method performs inference on the specified HBM in an amortized setup: once trained, it can readily be applied to a new data sample to compute the parameters' full posterior. We demonstrate the capability of our method on simulated data, as well as a challenging high-dimensional brain parcellation experiment. We also open up several questions that lie at the intersection between SBI techniques and structured Variational Inference.
翻译:通常, 人口研究以金字塔式组织数据为主, 使用高层次的贝叶斯模型(HBM), 富集板块。 在神经成形等环境中, 这些模型可能变得令人望而却步, 样本由在64 000个大脑位置、 4个测量课和至少数十个主题上测量的功能性 MRI 信号组成。 即使是在300个大脑位置的特定皮层区域, 其示例为100万个参数, 也妨碍了使用现代密度估计技术, 如模拟- 基于推断(SBI ) 。 在这种具有挑战性的问题类别中, 我们设计了一种新型的参数后方分布, 自动生成一个变异型家族, 自动生成一个与目标 HBM 相对立的双倍的变异式组合。 这个软体系系是一个神经网络, 结合一个基于关注的等级的分类组合组合组合组合, 向一套正常流动的组合输入摘要。 我们自动生成的神经网络, 利用板宽度的 HBMM(S) 及其参数空间。 由此产生的结构结构将它减少其比值与典型的比值的比值排序的大小排序,, 同时在测试中, 也将一个直判比重度上, 显示一个高的精确度 。