My research interests are mathematics of data science, graph-based learning and clustering, manifold learning, approximation theory via transformer neural networks, data-driven metrics for high-dimensional unsupervised learning, machine learning and their intersections. Below are the topics I have been worked on previously and currently.
Approximation for high dimensional functions via Kolmogorov superposition theorem
Nonparametric regression on manifolds via transformer neural networks
In-context learning via transformer neural networks
Compressed sensing and its application to signal recovery and image reconstruction
Graph-based learning and clustering
Graph Ricci curvature and its applications to data science
Physics informed neural networks for solving Poisson-Boltzmann equation
Low rank matrix cross approximationÂ
Out-of-distribution detection