因果影响的样本路径测度
A Sample Path Measure of Causal Influence
摘要：
我们提出了一个样本路径依赖的测量两个时间序列之间的因果关系的影响。所提出的测量是一个随机变量，其期望和是有向信息。所提出的措施的实现可以用于识别数据中的特定模式，这些模式产生从一个过程到另一个过程的更大的信息流，即使在静止过程中。我们演示了如何利用序贯预测理论在每个时间点获得准确的估计的因果措施，并引入了一个概念的遗憾评估的措施估计的性能。我们证明了一个有限的样本约束上的遗憾，这是由在获得估计的顺序预测的遗憾。我们估计的因果措施，使用贝叶斯更新方法的二进制马尔可夫过程的模拟收集。最后，考虑到该措施是一个时间的函数，我们演示了如何估计的因果措施可以扩展到有效地捕捉因果关系随时间变化的情况。
英文摘要：
We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify the specific patterns in the data that yield a greater flow of information from one process to another, even in stationary processes. We demonstrate how sequential prediction theory may be leveraged to obtain accurate estimates of the causal measure at each point in time and introduce a notion of regret for assessing the performance of estimators of the measure. We prove a finite sample bound on this regret that is determined by the regret of the sequential predictors used in obtaining the estimate. We estimate the causal measure for a simulated collection of binary Markov processes using a Bayesian updating approach. Finally, given that the measure is a function of time, we demonstrate how estimators of the causal measure may be extended to effectively capture causality in time-varying scenarios.
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