Identification of an influence network using ensemble-based filtering for Hawkes processes driven by count data

TL;DR

This paper introduces a scalable ensemble-based filtering method to infer influence networks from count data in event-driven systems, overcoming limitations of existing approaches in speed, data type, and network size.

Contribution

The authors develop a novel, parallelizable filtering approach for large-scale influence network inference from count data, without requiring prior physical network knowledge.

Findings

Effective for networks with up to 10,000 nodes

Works with count data, not just timestamps

Demonstrated on synthetic and real email data

Abstract

Many networks have event-driven dynamics (such as communication, social media and criminal networks), where the mean rate of the events occurring at a node in the network changes according to the occurrence of other events in the network. In particular, events associated with a node of the network could increase the rate of events at other nodes, depending on their influence relationship. Thus, it is of interest to use temporal data to uncover the directional, time-dependent, influence structure of a given network while also quantifying uncertainty even when knowledge of a physical network is lacking. Typically, methods for inferring the influence structure in networks require knowledge of a physical network or are only able to infer small network structures. In this paper, we model event-driven dynamics on a network by a multidimensional Hawkes process. We then develop a novel ensemble-based filtering approach for a time-series of count data (i.e., data that provides the number of events per unit time for each node in the network) that not only tracks the influence network structure over time but also approximates the uncertainty via ensemble spread. The method overcomes several deficiencies in existing methods such as existing methods for inferring multidimensional Hawkes processes are too slow to be practical for any network over ~50 nodes, can only deal with timestamp data (i.e. data on just when events occur not the number of events at each node), and that we do not need a physical network to start with. Our method is massively parallelizable, allowing for its use to infer the influence structure of large networks (~10,000 nodes). We demonstrate our method for large networks using both synthetic and real-world email communication data.