论文标题
关于因果网络标识的最大似然估计量的一致性
On the Consistency of Maximum Likelihood Estimators for Causal Network Identification
论文作者
论文摘要
我们考虑识别特定类别的马尔可夫链的参数的问题，称为Bernoulli自回归（BAR）过程。任何条形模型的结构均由有向图编码。向图中的节点的传入边缘表明特定时间的节点的状态受到上一段时间的相应父母节点的状态的影响。相关的边缘权重决定了每个父母节点的相应影响水平。在最简单的设置中，特定节点状态变量的Bernoulli参数是前一个时间瞬间中父母节点状态的凸组合和其他Bernoulli噪声随机变量。本文着重于使用最大似然（ML）估计的边缘权重识别问题，并证明了ML估计器对于条形模型的两个变体非常一致。我们还为上述两个变体提供了封闭形式的估计量，并证明了它们的强烈一致性。
We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph indicate that the state of the node at a particular time instant 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 random variable. This paper focuses on the problem of edge weight identification using Maximum Likelihood (ML) estimation and proves that the ML estimator is strongly consistent for two variants of the BAR model. We additionally derive closed-form estimators for the aforementioned two variants and prove their strong consistency.
