On the Consistency of Maximum Likelihood Estimators for Causal Network Identification
On the Consistency of Maximum Likelihood Estimators for Causal Network Identification
复制标题
DOI：
10.1109/cdc42340.2020.9304475
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Xiaotian Xie;Dimitrios Katselis;Carolyn L. Beck;R. Srikant
中科院分区：
文献类型：
--
作者：
Xiaotian Xie;Dimitrios Katselis;Carolyn L. Beck;R. Srikant
我们认为，根据一个特定的类马尔可夫链过程，称为伯努利自回归（BAR）过程的动态演变系统的数据识别参数的问题。任何BAR模型的结构都是由具有p个节点的有向图编码的。图的边缘表示因果影响，或等效的动态依赖性。更明确地说，图中节点的传入边指示节点在特定时刻的状态（其对应于伯努利随机变量）受到先前时刻的对应父节点的状态的影响。相关联的边权重确定来自每个父节点的相应影响水平。在最简单的设置中，特定节点的状态变量的伯努利参数是前一时刻的父节点状态和附加伯努利噪声变量的凸组合;该凸组合对应于相关联的父边缘权重和局部噪声变量的贡献。在本文中，我们专注于结构和边缘权重识别的问题，依靠完善的统计原理。我们提出了两个一致的估计的边缘权重，最大似然（ML）估计和封闭形式的估计，并数值证明，所得出的估计优于现有的算法在文献中的样本复杂性。
We consider the problem of identifying parameters from data for systems with dynamics evolving according to a particular class of Markov chain processes, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph with p nodes. The edges of the graph indicate causal influences, or equivalently dynamic dependencies. More explicitly, the incoming edges to a node in the graph indicate that the state of the node at a particular time instant, which corresponds to a Bernoulli random variable, is influenced by the states of the corresponding parental nodes in the previous time instant. The associated edge weights determine the corresponding level of influence from each parental node. In the simplest setup, the Bernoulli parameter of a particular node’s state variable is a convex combination of the parental node states in the previous time instant and an additional Bernoulli noise variable; this convex combination corresponds to the associated parental edge weights and the contribution of the local noise variable. In this paper, we focus on the problem of structure and edge weight identification by relying on well-established statistical principles. We present two consistent estimators of the edge weights, a Maximum Likelihood (ML) estimator and a closed-form estimator, and numerically demonstrate that the derived estimators outperform existing algorithms in the literature in terms of sample complexity.