CMX Student/Postdoc Seminar
I am currently a Postdoctoral Scholar Fellowship Trainee in Computing and Mathematical Sciences and NSF Postdoctoral Fellow at the California Institute of Technology sponsored by Profs. Venkat Chandrasekaran and Joel Tropp. I received my PhD in Mathematics in August 2019 from the University of Texas at Austin where I was fortunate to be advised by Prof. François Baccelli. My research interests lie broadly in the mathematics of data science. My work lies at the intersection of stochastic and convex geometry, high dimensional probability, and stochastic processes.
Many modern problems in data science aim to efficiently and accurately extract important features and make predictions from high dimensional and large data sets. Naturally occurring structure in the data underpins the success of many contemporary approaches, but large gaps between theory and practice remain. In this talk, I will present recent progress on two different methods for nonparametric regression that can be viewed as the projection of a lifted formulation of the problem with a simple stochastic or convex geometric description. In particular, I will first describe how the theory of stationary random tessellations in stochastic geometry addresses the computational and theoretical challenges of random decision forests with non-axis-aligned splits. Second, I will present a new approach to convex regression that returns non-polyhedral convex estimators compatible with semidefinite programming. These works open new questions at the intersection of stochastic and convex geometry, machine learning, and optimization.