通过匹配随机特征估计动态模型

中文摘要 AI 辅助

科学家越来越多地将他们的想法表达为复杂过程的动态模型。通常，模拟这些模型比计算它们产生特定结果的概率要容易得多，这使得基于似然性的估计变得不可行。现有的无似然性方法要么依赖于手动选择的摘要统计量，要么依赖于神经网络学习的表示。前者容易出错且费力，而后者计算量大，使许多科学家陷入困境。我们表明，对于一大类动态模型，可以通过匹配观测数据和模拟数据的少量随机特征来估计参数。具体来说，我们采用非线性动力学的结果表明，具有p维参数的模型通常可以从仅2p + 1个随机特征中识别出来。我们分别为平稳和非平稳过程引入了两个估计器，并在温和的正则条件下建立了它们的一致性。更广泛地说，我们的结果为一类新的基于模拟的估计和推理的随机特征方法奠定了基础。

英文摘要

Scientists increasingly express their ideas as dynamic models of complex processes. It is often much easier to simulate these models than to calculate the probability of their generating a particular outcome, making likelihood-based estimation infeasible. Existing likelihood-free approaches rely either on manually chosen summary statistics or on representations learned by neural networks. The former is error-prone and laborious, while the latter is computationally intensive, leaving many scientists in a difficult position. We show that, for a large class of dynamic models, parameters can be estimated by matching a small number of random features of the observed and simulated data. Specifically, we show that models with a $p$-dimensional parameter can be identified from just $2p+1$ generic random Fourier features. We introduce two estimators for stationary and nonstationary processes, respectively, and we establish their consistency under mild regularity conditions. More broadly, our results serve as the foundation for a new class of random feature methods for simulation-based estimation and inference.

发表机构

• Carnegie Mellon University（卡内基梅隆大学）

机构由 AI 辅助整理，请以论文原文为准。