The Block Point Process Model for Continuous-time Event-based Dynamic 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.

On the nature and use of models in network neuroscience

“…Less common, but potentially useful, theory-based models define edge dynamics, for example as generative network models [93]. These models could be profitably extended by recently developed dynamic extensions of the classic random graph, including the configuration model, the stochastic block model, and the block-point process model [94,95].…”

Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks

“…Users interact sequentially with items in many domains such as e-commerce (e.g., a customer purchasing an item) [48], education (a student enrolling in a MOOC course) [31], and social and collaborative platforms (a user posting in a group in Reddit) [19, 24]. The same user may interact with different items over a period of time and these interactions change over time [4, 5, 17, 21, 34, 37, 48]. These interactions create a network of temporal interactions between users and items .…”

Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels

“…Practitioners then inspect fitted parameters to understand inherent temporal dependencies, and perform downstream tasks such as prediction via simulation of the fitted processes [15], [17]. As inferring and interpreting (all) fitted Hawkes process parameters is crucial in many real-world applications [3], [6], [17]- [20], [22], we turn our attention to the challenges in fitting Hawkes process parameters, and especially, in estimating the decay parameter in the exponential kernel. Previous research has shown that the baseline µ and excitation jump α can be efficiently computed since the log-likelihood is amenable for convex optimization of these parameters [5], [18].…”

“…We begin by addressing the problem of quantifying the uncertainty of fitted decay values β, as well as potential consequences of mis-estimation on other Hawkes process parameters. One prominent application of multi-dimensional Hawkes processes consists in the estimation of directions of temporal dependency, e.g., when studying influence in online communities [17], [20], or in approximating complex geographical [3] or cortical [21] relationships. Recall that inferring such relations between a pair of Hawkes process dimensions may be framed as a problem of estimating which cross-excitation between the two dimensions is higher.…”

“…Such estimation approaches result in point estimates that can be considered as sufficient for simulating and predicting event streams. However, researchers frequently directly interpret Hawkes process parameters [3], [6], [18], [19], e.g., to infer the directions of temporal dependency [20]- [22]. Even though such applications rely on estimates of decay parameter values, the current state-of-the-art mostly neglects that, in practice, we derive these values only within a degree of certainty, in particular in a common case of a small number of realizations of a given process.…”