论文标题
连续Lyapunov模型的可识别性
Identifiability in Continuous Lyapunov Models
论文作者
论文摘要
最近引入的图形连续Lyapunov模型为相关多元数据的统计建模提供了一种新的方法。这些模型将每个观察结果视为平衡中多元动态过程的一次性横截面快照。通过求解通过动态过程的漂移矩阵参数化的连续lyapunov方程来获得数据的协方差矩阵。在这种情况下，不同的统计模型假定漂移矩阵中的不同稀疏模式，并且要阐明给定的稀疏性假设是否允许人们从数据的协方差矩阵中唯一恢复漂移矩阵参数，这将成为一个至关重要的问题。我们通过通过有向图表示稀疏性模式来研究此可识别性问题。我们的主要结果证明，当且仅当稀疏模式的图很简单时（即，不包含有向的两个循环）时，漂移矩阵在全球范围内可识别。此外，我们提出了通用性可识别性的必要条件，并提供了具有多达5个节点的小图的计算分类。
The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a one-time cross-sectional snapshot of a multivariate dynamic process in equilibrium. The covariance matrix for the data is obtained by solving a continuous Lyapunov equation that is parametrized by the drift matrix of the dynamic process. In this context, different statistical models postulate different sparsity patterns in the drift matrix, and it becomes a crucial problem to clarify whether a given sparsity assumption allows one to uniquely recover the drift matrix parameters from the covariance matrix of the data. We study this identifiability problem by representing sparsity patterns by directed graphs. Our main result proves that the drift matrix is globally identifiable if and only if the graph for the sparsity pattern is simple (i.e., does not contain directed two-cycles). Moreover, we present a necessary condition for generic identifiability and provide a computational classification of small graphs with up to 5 nodes.
