Modeling Inter-process Dynamics in Competitive Temporal Point Processes

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.