318 research outputs found
Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes
In this paper, we address the problem of fitting multivariate Hawkes
processes to potentially large-scale data in a setting where series of events
are not only mutually-exciting but can also exhibit inhibitive patterns. We
focus on nonparametric learning and propose a novel algorithm called MEMIP
(Markovian Estimation of Mutually Interacting Processes) that makes use of
polynomial approximation theory and self-concordant analysis in order to learn
both triggering kernels and base intensities of events. Moreover, considering
that N historical observations are available, the algorithm performs
log-likelihood maximization in operations, while the complexity of
non-Markovian methods is in . Numerical experiments on simulated
data, as well as real-world data, show that our method enjoys improved
prediction performance when compared to state-of-the art methods like MMEL and
exponential kernels
Correlated Cascades: Compete or Cooperate
In real world social networks, there are multiple cascades which are rarely
independent. They usually compete or cooperate with each other. Motivated by
the reinforcement theory in sociology we leverage the fact that adoption of a
user to any behavior is modeled by the aggregation of behaviors of its
neighbors. We use a multidimensional marked Hawkes process to model users
product adoption and consequently spread of cascades in social networks. The
resulting inference problem is proved to be convex and is solved in parallel by
using the barrier method. The advantage of the proposed model is twofold; it
models correlated cascades and also learns the latent diffusion network.
Experimental results on synthetic and two real datasets gathered from Twitter,
URL shortening and music streaming services, illustrate the superior
performance of the proposed model over the alternatives
Bursting activity spreading through asymmetric interactions
People communicate with those who have the same background or share a common
interest by using a social networking service (SNS). News or messages propagate
through inhomogeneous connections in an SNS by sharing or facilitating
additional comments. Such human activity is known to lead to endogenous
bursting in the rate of message occurrences. We analyze a multi-dimensional
self-exciting process to reveal dependence of the bursting activity on the
topology of connections and the distribution of interaction strength on the
connections. We determine the critical conditions for the cases where
interaction strength is regulated at either the point of input or output for
each person. In the input regulation condition, the network may exhibit
bursting with infinitesimal interaction strength, if the dispersion of the
degrees diverges as in the scale-free networks. In contrast, in the output
regulation condition, the critical value of interaction strength, represented
by the average number of events added by a single event, is a constant
, independent of the degree dispersion. Thus, the
stability in human activity crucially depends on not only the topology of
connections but also the manner in which interactions are distributed among the
connections.Comment: 8 pages, 8 figure
Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data
We propose a novel class of network models for temporal dyadic interaction
data. Our goal is to capture a number of important features often observed in
social interactions: sparsity, degree heterogeneity, community structure and
reciprocity. We propose a family of models based on self-exciting Hawkes point
processes in which events depend on the history of the process. The key
component is the conditional intensity function of the Hawkes Process, which
captures the fact that interactions may arise as a response to past
interactions (reciprocity), or due to shared interests between individuals
(community structure). In order to capture the sparsity and degree
heterogeneity, the base (non time dependent) part of the intensity function
builds on compound random measures following Todeschini et al. (2016). We
conduct experiments on a variety of real-world temporal interaction data and
show that the proposed model outperforms many competing approaches for link
prediction, and leads to interpretable parameters
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