Network Clocks: Detecting the Temporal Scale of Information Diffusion

Information diffusion models typically assume a discrete timeline in which an information token spreads in the network. Since users in real-world networks vary significantly in their intensity and periods of activity, our objective in this work is to answer: How to determine a temporal scale that best agrees with the observed information propagation within a network? A key limitation of existing approaches is that they aggregate the timeline into fixed-size windows, which may not fit all network nodes' activity periods. We propose the notion of a heterogeneous network clock: a mapping of events to discrete timestamps that best explains their occurrence according to a given cascade propagation model. We focus on the widely-adopted independent cascade (IC) model and formalize the optimal clock as the one that maximizes the likelihood of all observed cascades. The single optimal clock (OC) problem can be solved exactly in polynomial time. However, we prove that learning multiple optimal clocks (kOC), corresponding to temporal patterns of groups of network nodes, is NP-hard. We propose scalable solutions that run in almost linear time in the total number of cascade activations and discuss approximation guarantees for each variant. Our algorithms and their detected clocks enable improved cascade size classification (up to 8% F1 lift) and improved missing cascade data inference (0.15 better recall). We also demonstrate that the network clocks exhibit consistency within the type of content diffusing in the network and are robust with respect to the propagation probability parameters of the IC model.