Research Interests
The overall goal of my research is to use the theory of partial differential equations (PDEs) and the calculus of variations to study foundational problems in machine learning and data science, and develop new, more efficient, algorithms founded on strong theoretical principles. Much of my work involves proving large sample size continuum limits for discrete problems. In this context, the continuum is the big data limit of discrete machine learning, and tools from continuum analysis can be used to understand why algorithms work well, and when they will fail. It is particularly exciting when this kind of analysis leads to new algorithms with performance guarantees.
Research Website
