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Register a new userDynamic Hawkes Processes for Discovering Time-evolving Communities States behind Diffusion Processes
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Added by
Maya Okawa
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g., regions, online user groups). Modeling diffusion processes and predicting future events are crucial in many applications including epidemic control, viral marketing, and predictive policing. Hawkes processes offer a central tool for modeling the diffusion processes, in which the influence from the past events is described by the triggering kernel. However, the triggering kernel parameters, which govern how each community is influenced by the past events, are assumed to be static over time. In the real world, the diffusion processes depend not only on the influences from the past, but also the current (time-evolving) states of the communities, e.g., peoples awareness of the disease and peoples current interests. In this paper, we propose a novel Hawkes process model that is able to capture the underlying dynamics of community states behind the diffusion processes and predict the occurrences of events based on the dynamics. Specifically, we model the latent dynamic function that encodes these hidden dynamics by a mixture of neural networks. Then we design the triggering kernel using the latent dynamic function and its integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a flexible way to learn complex representations of the time-evolving communities states, while at the same time it allows to computing the exact likelihood, which makes parameter learning tractable. Extensive experiments on four real-world event datasets show that DHP outperforms five widely adopted methods for event prediction.
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The contagion dynamics can emerge in social networks when repeated activation is allowed. An interesting example of this phenomenon is retweet cascades where users allow to re-share content posted by other people with public accounts. To model this type of behaviour we use a Hawkes self-exciting process. To do it properly though one needs to calibrate model under consideration. The main goal of this paper is to construct moments method of estimation of this model. The key step is based on identifying of a generator of a Hawkes process. We perform numerical analysis on real data as well.
Modeling online discourse dynamics is a core activity in understanding the spread of information, both offline and online, and emergent online behavior. There is currently a disconnect between the practitioners of online social media analysis -- usually social, political and communication scientists -- and the accessibility to tools capable of examining online discussions of users. Here we present evently, a tool for modeling online reshare cascades, and particularly retweet cascades, using self-exciting processes. It provides a comprehensive set of functionalities for processing raw data from Twitter public APIs, modeling the temporal dynamics of processed retweet cascades and characterizing online users with a wide range of diffusion measures. This tool is designed for researchers with a wide range of computer expertise, and it includes tutorials and detailed documentation. We illustrate the usage of evently with an end-to-end analysis of online user behavior on a topical dataset relating to COVID-19. We show that, by characterizing users solely based on how their content spreads online, we can disentangle influential users and online bots.
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to three key hypotheses: parametric, linear and homogeneous. Recent work has attempted to address these limitations separately. This work aims to overcome all three assumptions simultaneously by proposing the flexible state-switching Hawkes processes: a flexible, nonlinear and nonhomogeneous variant where a state process is incorporated to interact with the point processes. The proposed model empowers Hawkes processes to be applied to time-varying systems. For inference, we utilize the latent variable augmentation technique to design two efficient Bayesian inference algorithms: Gibbs sampler and mean-field variational inference, with analytical iterative updates to estimate the posterior. In experiments, our model achieves superior performance compared to the state-of-the-art competitors.
Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events will happen next and when. A de facto standard mathematical framework to do this is the Hawkes process. In order to enhance expressivity of multivariate Hawkes processes, conventional statistical methods and deep recurrent networks have been employed to modify its intensity function. The former is highly interpretable and requires small size of training data but relies on correct model design while the latter has less dependency on prior knowledge and is more powerful in capturing complicated patterns. We leverage pros and cons of these models and propose a self-attentive Hawkes process(SAHP). The proposed method adapts self-attention to fit the intensity function of Hawkes processes. This design has two benefits:(1) compared with conventional statistical methods, the SAHP is more powerful to identify complicated dependency relationships between temporal events; (2)compared with deep recurrent networks, the self-attention mechanism is able to capture longer historical information, and is more interpretable because the learnt attention weight tensor shows contributions of each historical event. Experiments on four real-world datasets demonstrate the effectiveness of the proposed method.
This work builds a novel point process and tools to use the Hawkes process with interval-censored data. Such data records the aggregated counts of events solely during specific time intervals -- such as the number of patients admitted to the hospital or the volume of vehicles passing traffic loop detectors -- and not the exact occurrence time of the events. First, we establish the Mean Behavior Poisson (MBP) process, a novel Poisson process with a direct parameter correspondence to the popular self-exciting Hawkes process. The event intensity function of the MBP is the expected intensity over all possible Hawkes realizations with the same parameter set. We fit MBP in the interval-censored setting using an interval-censored Poisson log-likelihood (IC-LL). We use the parameter equivalence to uncover the parameters of the associated Hawkes process. Second, we introduce two novel exogenous functions to distinguish the exogenous from the endogenous events. We propose the multi-impulse exogenous function when the exogenous events are observed as event time and the latent homogeneous Poisson process exogenous function when the exogenous events are presented as interval-censored volumes. Third, we provide several approximation methods to estimate the intensity and compensator function of MBP when no analytical solution exists. Fourth and finally, we connect the interval-censored loss of MBP to a broader class of Bregman divergence-based functions. Using the connection, we show that the current state of the art in popularity estimation (Hawkes Intensity Process (HIP) (Rizoiu et al.,2017b)) is a particular case of the MBP process. We verify our models through empirical testing on synthetic data and real-world data. We find that on real-world datasets that our MBP process outperforms HIP for the task of popularity prediction.
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