1,264 research outputs found
Multivariate Hawkes Processes for Large-scale Inference
In this paper, we present a framework for fitting multivariate Hawkes
processes for large-scale problems both in the number of events in the observed
history and the number of event types (i.e. dimensions). The proposed
Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of
the kernel matrix that allows to perform the nonparametric learning of the
triggering kernels using at most operations, where is the
rank of the approximation (). This comes as a major improvement to
the existing state-of-the-art inference algorithms that are in .
Furthermore, the low-rank approximation allows LRHP to learn representative
patterns of interaction between event types, which may be valuable for the
analysis of such complex processes in real world datasets. The efficiency and
scalability of our approach is illustrated with numerical experiments on
simulated as well as real datasets.Comment: 16 pages, 5 figure
Shaping Social Activity by Incentivizing Users
Events in an online social network can be categorized roughly into endogenous
events, where users just respond to the actions of their neighbors within the
network, or exogenous events, where users take actions due to drives external
to the network. How much external drive should be provided to each user, such
that the network activity can be steered towards a target state? In this paper,
we model social events using multivariate Hawkes processes, which can capture
both endogenous and exogenous event intensities, and derive a time dependent
linear relation between the intensity of exogenous events and the overall
network activity. Exploiting this connection, we develop a convex optimization
framework for determining the required level of external drive in order for the
network to reach a desired activity level. We experimented with event data
gathered from Twitter, and show that our method can steer the activity of the
network more accurately than alternatives
Uncovering Causality from Multivariate Hawkes Integrated Cumulants
We design a new nonparametric method that allows one to estimate the matrix
of integrated kernels of a multivariate Hawkes process. This matrix not only
encodes the mutual influences of each nodes of the process, but also
disentangles the causality relationships between them. Our approach is the
first that leads to an estimation of this matrix without any parametric
modeling and estimation of the kernels themselves. A consequence is that it can
give an estimation of causality relationships between nodes (or users), based
on their activity timestamps (on a social network for instance), without
knowing or estimating the shape of the activities lifetime. For that purpose,
we introduce a moment matching method that fits the third-order integrated
cumulants of the process. We show on numerical experiments that our approach is
indeed very robust to the shape of the kernels, and gives appealing results on
the MemeTracker database
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