平稳设定下VAR(1)模型的可辨识性
Identifiability of VAR(1) model in a stationary setting
AI总结：
研究从平稳分布中辨识VAR(1)模型的有向加权图结构，利用代数统计中的雅可比拟阵方法，给出不同图产生不同稳态分布的充分图条件。
摘要：
我们考虑经典的一阶向量自回归（VAR(1)）模型，其中将自回归交互矩阵解释为VAR(1)过程分量之间的影响关系，该关系可由加权有向图编码。以往大部分工作基于时间序列观测研究图的结构可辨识性，因此依赖于动态信息。本文假设存在平衡态，转而研究从平稳分布中辨识图的可辨识性，即寻求仅利用静态信息重建动态网络底层影响图的方法。我们采用代数统计的方法，通过模型参数化相关的雅可比拟阵来刻画模型，并引入充分的图条件，使得不同图产生不同的稳态分布。此外，我们展示了结果如何应用于刻画受生态研究启发的网络。
英文摘要：
We consider a classical First-order Vector AutoRegressive (VAR(1)) model, where we interpret the autoregressive interaction matrix as influence relationships among the components of the VAR(1) process that can be encoded by a weighted directed graph. A majority of previous work studies the structural identifiability of the graph based on time series observations and therefore relies on dynamical information. In this work we assume that an equilibrium exists, and study instead the identifiability of the graph from the stationary distribution, meaning that we seek a way to reconstruct the influence graph underlying the dynamic network using only static information. We use an approach from algebraic statistics that characterizes models using the Jacobian matroids associated with the parametrization of the models, and we introduce sufficient graphical conditions under which different graphs yield distinct steady-state distributions. Additionally, we illustrate how our results could be applied to characterize networks inspired by ecological research.
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