基于矩约束下嵌入归一化流和隐含经验概率组合的基于模拟的参数估计
Simulation-based parameter estimation via a combination of embedded normalizing flows and implied empirical probabilities under moment restrictions
- 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总结：
针对物理系统计算模拟模型，提出含嵌入归一化流和经验似然估计两步的参数估计框架，利用一阶梯度方法更新参数，其参数化嵌入归一化流的逆可作替代模型，用于量化模型差异与敏感性分析。
AI中文摘要：
在这项工作中，我们为一个由物理系统的计算模拟定义的模型提出了一个基于模拟的参数估计框架。具体概述了一个由两个紧密集成步骤组成的估计框架，以促进整体端到端的参数估计方案。第一步利用嵌入归一化流将残差信息的未知复杂分布转换为对应变换后残差信息的简单基础分布。第二步在矩约束下利用经验似然估计器对基础分布施加间接约束，将变换后的残差信息视为离散分布总体产生的随机变量。还使用一阶梯度方法更新由计算模拟和相应参数化嵌入归一化流定义的模型的估计参数值，通过利用经验似然函数的隐式微分获取所有梯度相关信息。此外，参数化嵌入归一化流关于估计参数值的逆作为计算模拟模型的替代模型，为量化模型差异和敏感性分析提供有用信息。
英文摘要：
In this work, we present a simulation-based parameter estimation framework for a model defined by a computational simulation of a physical system. We specifically outline an estimation framework consisting of two closely-integrated steps that facilitate an overall end-to-end parameter estimation scheme. The first step involves utilizing an embedded normalizing flow which is used to transform the unknown complex distribution of the residual information into a simple base distribution corresponding to the transformed residual information. In the second step, an empirical-likelihood estimator, under moment restrictions, is utilized for imposing an indirect constrain on the base distribution, where such an instantiated task reasonably allows us to treat the transformed residual information as random variables arising from discretely distribution population with each transformed data point as a single-cell from a set of finite-cell contingencies. Moreover, we use first-order gradient methods for updating the estimated parameter values of the model defined by the computational simulation and the corresponding parametrized embedded normalizing flow, that call for all gradient-related information by leveraging implicitly differentiations of the empirical-likelihood function, which is constructed from the implied empirical probabilities under moment restrictions. Here, it is worth mentioning that the problem formulation presented in this work, which highlights an information-theoretic interpretation, allows to present a computational framework for algorithmic implementations. Finally, as a-by-product, the inverse of the parametrized embedded normalizing flow, w.r.t. the estimated parameter values, serves as a surrogate model for the computational simulation model, which provides useful information for quantifying model discrepancies and sensitivity analysis.
