GRADUATE STUDENT SEMINAR: Phase transitions in soft random geometric graphs, Suqi Liu, ORFE

Phase transitions in soft random geometric graphs

Abstract: Random graphs with latent geometric structure, where the edges are generated depending on some unobserved random vectors, find broad applications in social studies, wireless communications, and biological sciences. As a first step to understand these models, the question of when they are different from random graphs with independent edges, i.e., Erdos-Renyi graphs, has been studied recently. It was shown for a particular spherical random geometric graph model that the geometry cannot be detected when the dimension of the latent space becomes high. In this talk, we focus on generalizations of this result to soft random geometric graphs. We consider general connection functions and view them as different types of noise in the geometric graphs. We show that there is a trade-off between dimensionality and noise in detecting geometry in the random graphs. The talk is based on joint work with Professor Miklos Racz.  

Speaker: Suqi Liu, is a Ph.D. student at ORFE, Princeton University working with Professor Miklos Racz. His research interests lie broadly in probability, high-dimensional statistics, and combinatorics. Specifically, he studies random graphs with latent geometric structure with applications to network science. Previously, Suqi was a graduate student at UC San Diego advised by Professor Lawrence Saul, co-advised by Professor Geoffrey Voelker and Professor Stefan Savage. He completed his undergraduate study at Tsinghua University under the supervision of Professor Jun Zhu. Suqi worked on Google Knowledge Graph and Google Ads at Google in the Bay Area during the summers of 2016 and 2018. He also interned at Microsoft Research Asia from April to November 2012.