My research focuses on using convex and non-convex optimization methods to model and solve problems in signal and information processing, physical sciences, and machine learning. I am especially interested in designing optimization procedures that come with theoretical performance guarantees and are scalable to large data sets. A common theme of my work is leveraging prior structures and domain knowledge in a computationally effective way; these structures could be sparsity, manifold, smoothness, dynamics, graphs, and so on. One of the most interesting parts of this work is to explore the trade-offs between computational time, statistical performance, and sampling complexity. A few current projects include landscape analysis of nonconvex and distributed optimizations; convex optimization for blind inverse problems; expressivity, trainability, and generalization of deep neural networks; tensor decomposition and completion; super-resolution imaging; and spectral estimation.

News 2017