Dynamic reconstruction of influence graphs with adaptive directed information

We introduce an adaptive version of directed information to estimate an influence graph over nodes with time-varying features. Originally developed as a generalization of the Shannon Mutual Information for quantifying the effect of feedback in a simple communication channel, directed information (DI) measures the amount of causal, time-varying influence that one node's actions have on another node. By estimating these quantities, we can infer a directed graph that captures the flow of influence between nodes. We introduce an online time-averaged version of DI called adaptive directed information (ADI) to study the difference in graphical structure over time. This method is applied to two Twitter US political datasets to track changes in the graphical structure between candidates' Twitter feeds.