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

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.Comment: To appear at The Web Conference 201

Latent Self-Exciting Point Process Model for Spatial-Temporal Networks

We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a scenario where certain interaction events lack information about participants. Instead, this information needs to be inferred from the available observations. We develop an efficient approximate algorithm based on variational expectation-maximization to infer unknown participants in an event given the location and the time of the event. We validate the model on synthetic as well as real-world data, and obtain very promising results on the identity-inference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares favorably with baseline approaches.Comment: 20 pages, 6 figures (v3); 11 pages, 6 figures (v2); previous version appeared in the 9th Bayesian Modeling Applications Workshop, UAI'1

Efficient inference for nonparametric hawkes processes using auxiliary latent variables

© 2020 Feng Zhou, Zhidong Li, Xuhui Fan, Yang Wang, Arcot Sowmya and Fang Chen. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v21/19-930.html. The expressive ability of classic Hawkes processes is limited due to the parametric assumption on the baseline intensity and triggering kernel. Therefore, it is desirable to perform inference in a data-driven, nonparametric approach. Many recent works have proposed nonparametric Hawkes process models based on Gaussian processes (GP). However, the likelihood is non-conjugate to the prior resulting in a complicated and time-consuming inference procedure. To address the problem, we present the sigmoid Gaussian Hawkes process model in this paper: the baseline intensity and triggering kernel are both modeled as the sigmoid transformation of random trajectories drawn from a GP. By introducing auxiliary latent random variables (branching structure, Pólya-Gamma random variables and latent marked Poisson processes), the likelihood is converted to two decoupled components with a Gaussian form which allows for an efficient conjugate analytical inference. Using the augmented likelihood, we derive an efficient Gibbs sampling algorithm to sample from the posterior; an efficient expectation-maximization (EM) algorithm to obtain the maximum a posteriori (MAP) estimate and furthermore an efficient mean-field variational inference algorithm to approximate the posterior. To further accelerate the inference, a sparse GP approximation is introduced to reduce complexity. We demonstrate the performance of our three algorithms on both simulated and real data. The experiments show that our proposed inference algorithms can recover well the underlying prompting characteristics efficiently

Modeling and estimation of multi-source clustering in crime and security data

While the presence of clustering in crime and security event data is well established, the mechanism(s) by which clustering arises is not fully understood. Both contagion models and history independent correlation models are applied, but not simultaneously. In an attempt to disentangle contagion from other types of correlation, we consider a Hawkes process with background rate driven by a log Gaussian Cox process. Our inference methodology is an efficient Metropolis adjusted Langevin algorithm for filtering of the intensity and estimation of the model parameters. We apply the methodology to property and violent crime data from Chicago, terrorist attack data from Northern Ireland and Israel, and civilian casualty data from Iraq. For each data set we quantify the uncertainty in the levels of contagion vs. history independent correlation.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS647 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org