I am interested in the mathematical foundations of data science. Some of the topics I am currently working on include:
a. Randomized Algorithms
Randomization is a common approach to approximately solving problems constrained by computational complexity. My work in this area involves applying random projection-based techniques (e.g., sketching) to problems in numerical approximation, statistical learning, and discrete optimization.
b. Network Data Analysis
The Plackett-Luce model has been widely used in comparison data analysis, with applications in choice modeling, horse racing, sports analytics, etc. My research develops a unified asymptotic theory of the Plackett--Luce model and its variants.
c. Multifidelity Methods
Multifidelity methods leverage models with varying accuracies and costs to produce outputs with enhanced accuracy than relying on a single model alone, subject to a computational budget constraint. My work combines bandit learning to design principled data assimilation methods for computational tasks in forward uncertainty quantification.
I am also involved in collaboration with people from computer science and engineering. I am often problem-driven and eager to learn new ideas (which I believe to be one of the most rewarding aspects of research). If you are interested in any of these topics or have an intriguing problem you'd like to discuss, please feel free to send me an email.
