发表机构
The Catholic University of America（美国天主教大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于聚合归一化流链的似然逼近新视角，结合经验似然与序贯决策，实现高效参数探索、样本生成及贝叶斯推断，支持假设检验与不确定性量化。
AI 中文摘要
我们在基于模拟的推断框架内提出了关于似然逼近问题的新视角，该视角促进了大规模数据分析中可扩展且可控的模拟程序，允许高效的参数空间探索或高维空间中的平滑插值，从而支持假设检验和不确定性量化的有效统计处理。具体而言，我们考虑使用由$n$个聚合归一化流组成的链进行似然逼近的方案，其中来自前向复杂模拟模型的一组预先复制的观测数据集首先通过第一组双射变换，随后依次通过其余各组双射变换。这里，我们假设对于任意$k \in \{1, 2, \ldots, n\}$，与前$k$组双射变换对应的参数以某种最优性意义下被顺序估计，以构造灵活的的概率分布，而无需考虑剩余的$(n-k)$组双射变换。此外，我们关注的重点是强调两个互补的数学论证：一个利用基于矩约束下的经验似然估计器的信息论形式化，另一个采用带有混合分布的序贯决策范式，用于更新和聚合整个归一化流的估计参数。作为副产品，该框架提供了一个可靠的替代模型，该模型以定义前向计算模拟的模型参数为条件，允许具有统计效力的样本生成，并在贝叶斯推断、假设检验和不确定性量化范式中促进计算上易处理的方案。
英文摘要
We present a new perspective on the problem of likelihood approximation within the framework of simulation-based inference that promotes scalable and controllable simulation routines for large-scale data analysis, allows efficient parameter space exploration or smooth interpolation in high-dimensions and, thus, supports valid statistical treatments of hypothesis testings as well as uncertainty quantification. In particular, we consider a chain of $n$-aggregated normalizing flows for likelihood approximation scheme, where a set of upfront replicated observation datasets from the forward complex simulation model pass through the first set of bijective transformations, and then subsequently pass to the other sets of bijective transformations. Here, we assume that, for any $k \in \{1,\,2, \ldots, n\}$, the parameters corresponding to the first $k$ sets of bijective transformations are estimated sequentially, in some sense of optimality, for constructing flexible probability distributions, regardless of the remaining $(n-k)$ sets of bijective transformations. Moreover, our objects of interest are to highlight two complementary mathematical arguments that leverage an informatics-theoretic formalization, based-on empirical likelihood estimators under moment restrictions, and a sequential decision-making paradigm, with mixing distributions, for updating and aggregating the estimated parameters of the overall normalizing flows. As a by-product, the framework provides a reliable surrogate model, conditioned on the model parameters defining the forward computational simulation, that allows samples generation, with statistical powers, and facilitates computationally tractable scheme in the Bayesian paradigm for inference, hypothesis testings and uncertainty quantification.
Comments17 pages, 1 figure
