Research

I mostly work on probabilistic aspects of geometric graphs and their applications in statistics. 

My first PhD project looked at two-sample tests based on geometric graphs. Perhaps the most well known example of such tests is the Friedman-Rafsky test. These tests involve constructing geometric graphs out of the available data and using the graph to generate the test statistic. During this project, I worked on describing the regimes where these tests are powerful as well studying their behavior in high dimensional settings.

My paper Power properties of the two-sample test based on the nearest neighbors graph has been accepted for publication at Annals of Statistics. You can check it out on ArXiv.

At present, I am working on studying connectivity properties of nearest neighbors graphs coming from high-dimensional distributions. Empirically, it can be observed that when the dimension is sufficiently large compared to the sample size, the 1-nearest neighbors graph is disconnected with high probability while the 2-nearest neighbors graph is connected with high probability. This is a surprising phenomenon which goes contrary to what has been shown in many commonly studied random graph models. My work involves describing the interplay between dimension and sample size which causes this behavior.