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...equence of recent work has argued that modeling cascade data and information diffusion using continuous-time diffusion networks can provide significantly more accurate models than discretetime models =-=[8, 9, 10, 11, 12, 13, 14, 15]-=-. There is a twofold rationale behind this modeling choice. First, since follow-ups occur asynchronously, continuous variables seem more appropriate to represent them. Artificially discretizing the ti...

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...citation, where a user simply follows what his neighbors are doing due to peer pressure. These social phenomena have been made analogy to the occurrence of earthquake [18] and the spread of epidemics =-=[19]-=-, and can be well-captured by multivariate Hawkes processes [6] as shown in a number of recent works (e.g., [7, 8, 9, 10, 11, 12]). More specifically, a multivariate Hawkes process is a counting proce...

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...processes assume that all the previous instances (i.e., reshares) influence the future evolution of the process. Self-exciting point processes are frequently used to model “rich get richer” phenomena =-=[22, 23, 33, 36]-=-. They are ideal for modeling information cascades in networks because every new reshare of a post not only increases its cumulative reshare count by one, but also exposes new followers who may furthe...

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...red by their latent variable set-up, we adapted some of their hidden variable formulation within the marked point process framework into our fully Bayesian inference setting. We have leveraged ideas from previous work on self-exciting processes to consequently treating the levels of excitation as random processes. Linderman and Adams (2014) introduced a multivariate point process combining self (Hawkes) and external (Cox) flavors to study latent networks in the data. These processes have also been proposed and applied in analyzing topic diffusion and user interactions (Rodriguez et al., 2011; Yang and Zha, 2013). Farajtabar et al. (2014) put forth a temporal point process model with one intensity being modulated by the other. Bounds of self exciting processes are also studied in (Hansen et al., 2015). Differently from these, we breathe another dimension into Hawkes processes by modeling the contagion parameters as a stochastic differential equation equipped with general procedures for learning. This allows much more latitude in parameterizing the self-exciting processes as a basic building block before incorporating wider families of processes. Studies of inference for continuous SDEs have been launc...

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...we consider are Hawkes processes, a class of interacting point processes customarily used to describe self and cross-excitation phenomena [17, 18]. For a long time, Hawkes models have been extensively used to describe the occurrence of earthquakes in some given region [19, 20]. They are getting more and more popular in many other applications in which tracking how information diffuses through different “agents” is the main concern, e.g., neurobiology (neurons activity) [21], sociology (spread of terrorist activity) [22, 23] or processes on the internet (viral diffusion across social networks) [24, 25]. Their application to finance can be 5 traced back to Refs [26, 27], and has been followed by a still-ongoing spree of activity [28, 29, 30, 31, 32, 7, 8, 33, 34, 10, 9]. An N -dimensional Hawkes process is defined by a set of N counting processes evolving in continuous time X(t) = {Xi(t)}Ni=13. The probability for an event to be triggered is expressed by a stochastic intensity function Λ(t) = {Λi(t)}Ni=1 which evolves according to the dynamics: Λ(t) = µ+ ∫ t −∞ Φ(t− t′)dX(t′) , (13) where the components of µ are commonly referred as exogenous intensities (or baseline intensities), and Φ(t) i...

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...er user. Given the heterogeneity of the network activity and target shape, this is a significant improvement over the baselines. Appendix F includes further results on varying number of nodes, number of stages, and duration of each stage. Campaigning results on real world networks. We also evaluate the proposed framework on real world data. To this end, we utilize the MemeTracker dataset [9] which contains the information flows captured by hyperlinks between different sites with timestamps during 9 months. This data has been previously used to validate Hawkes process models of social activity [5, 10]. For the real data, we utilize two evaluation procedures. First, similar to the synthetic case, we simulate the network, but now on a network based on the learned parameters from real data. However, the more interesting evaluation scheme would entail carrying out real intervention in a social media platform. Since this is very challenging to do, instead, in this evaluation scheme we used held-out data to mimic such procedure. Second, we form 10 pairs of clusters/cascades by selecting any 2 combinations of 5 largest clusters in the Memetracker data. Each is a cascade of events around a common ...

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...ynamics, and proved that the Hawkes process has a promising predictive power. Inspired by this work, many derivative models have been proposed in recent years to solve various problems in social media=-=[17, 32, 16, 34, 1]-=-. Most models just implement a single self-excited Hawkes process, while the real world is too complicated to be comprehensively represented by a single process This paper also implements Hawkes proce...

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... et al. [3], Jaisson-Rosenbaum [21]), social networks interactions (Blundell et al. [7], Simma-Jordan [36], Zhou et al. [38]) and epidemiology like for instance viral diffusion on a network (Hang-Zha =-=[37]-=-), to name but a few. In all these contexts, observations are often represented as events (like spikes or features) associated to agents or nodes on a given network, and that arrive randomly through t...

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...Social networks, Hawkes processes, nonnegative matrix factorization 1. INTRODUCTION There has been a steady increase of interest in point processes for modeling information diffusion in networks (see =-=[16, 25, 29, 31, 32]-=-). Information diffusion is a phenomenon in social networks where users broadcast information to others in the network; for example on Twitter, users can ”tweet”. By tweeting, users broadcast informat...