论文标题
动态网络的结构建模并确定最大可能性
Structural Modelling of Dynamic Networks and Identifying Maximum Likelihood
论文作者
论文摘要
本文考虑了非线性动态模型，其中感兴趣的主要参数是表征网络（传染）效应的非负矩阵。通常，通过假设有限数量的非零元素（稀疏性）或考虑降低非负矩阵分解（NMF）的等级方法来限制该网络矩阵。我们遵循后一种方法，并开发了一种新的概率NMF方法。我们引入了一种新的识别最大可能性（IML）方法，以一致地估计已识别的可允许的NMF集合并得出其渐近分布。此外，我们提出了给定非负等级的参数矩阵的最大似然估计器，得出其渐近分布和相关效率结合。
This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of nonzero elements (sparsity), or by considering a reduced rank approach for nonnegative matrix factorization (NMF). We follow the latter approach and develop a new probabilistic NMF method. We introduce a new Identifying Maximum Likelihood (IML) method for consistent estimation of the identified set of admissible NMF's and derive its asymptotic distribution. Moreover, we propose a maximum likelihood estimator of the parameter matrix for a given non-negative rank, derive its asymptotic distribution and the associated efficiency bound.
