The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks

TL;DR

This paper introduces the block point process model (BPPM) for analyzing continuous-time dynamic networks, capturing timestamped relational events more effectively than static models, and demonstrates its application on large real-world social network data.

Contribution

The paper proposes a novel BPPM for continuous-time networks, linking it to SBM in large networks, and develops efficient inference methods for real data analysis.

Findings

BPPM accurately models real-world social network data.

Networks generated by BPPM follow SBM in the large-node limit.

Efficient inference procedures enable analysis of large-scale networks.

Abstract

We consider the problem of analyzing timestamped relational events between a set of entities, such as messages between users of an on-line social network. Such data are often analyzed using static or discrete-time network models, which discard a significant amount of information by aggregating events over time to form network snapshots. In this paper, we introduce a block point process model (BPPM) for continuous-time event-based dynamic networks. The BPPM is inspired by the well-known stochastic block model (SBM) for static networks. We show that networks generated by the BPPM follow an SBM in the limit of a growing number of nodes. We use this property to develop principled and efficient local search and variational inference procedures initialized by regularized spectral clustering. We fit BPPMs with exponential Hawkes processes to analyze several real network data sets, including a Facebook wall post network with over 3,500 nodes and 130,000 events.