Branching Processes and their Application to Popularity Dynamics

Abstract

Arising from a desire to understand the likelihood of a family name becoming extinct, branching processes have a rich history and have been shown to be applicable to a wide range of domains. The simplest description of these processes is the case where a parent has a random number of children during their lifetime who themselves proceed to have a similarly distributed number of children. In this talk I demonstrate how the processes may be used to describe social spreading phenomena whereby the parents are now online pieces of information (tweets, online threads, …) while their children correspond to interactions with these pieces (retweets, comments,…) and as such may represent social contagion dynamics. Two specific examples will be considered in detail, the first being a mathematical model of online spreading across multiple social media platforms and the effect said network structure has upon the dynamics. Second, I will demonstrate how a branching process approach can allow a unified understanding of the well-studied Hawkes process (which has itself been shown to accurately describe social spreading features) and may in fact allow one to make predictions regarding future dynamics of such processes.

Joey O'Brien

Senior Quantitative Analyst

Senior Consultant in quantitative finance and data science for Acadia, working in R and Python.