Modeling Inter‑process Dynamics in Competitive Temporal Point Processes

Abstract

Temporal point processes (TPPs) have become ubiquitous
in research in recent years, with applications ranging from analysis of
online information diffusion to networking systems. These processes
comprise a series of discrete events localized in continuous time. In
several cases, it is observed that multiple processes are realized in the
same time-span which are likely to influence each other, often in a competitive
way. In the case of hashtag diffusion in Twitter, the mentions of
several hashtags related to the same event constitute a set of mutually
interacting processes which exhibit competitive dynamics. In the case of
Amazon product reviews, the review streams of similar products constitute
a set of related processes which may compete with each other due
to brand competition between products. In the case of computer network
traffic, the packet streams generated by hosts on the same network
constitute mutually influencing processes which also exhibit competition
due to link bandwidth constraints. Whereas several works have tried to
model these processes individually, joint modeling of such processes
along with their interactions has not been explored in the literature very
well. In this work, we survey a few emerging techniques developed by
the authors which deal with modeling such joint interactive processes.
These techniques show that with simple modifications to known techniques
of neural TPP modeling, it is possible to model the interactions
between concurrent processes effectively. Such methods also yield substantial
improvements over the existing methods which seek to model
individual processes without considering the joint interactions between
them.