Associate Professor in the Department of Electrical and Computer Engineering
My research interests lie at the intersection of signal processing, statistics, and information theory, with applications in high-dimensional statistical inference, compressed sensing, and machine learning. A unifying theme throughout my work is to first obtain precise characterizations of the fundamental limits and to then use this fundamental understanding to inform the design and analysis of practical methods. Specific directions include:
- Interdisciplinary mathematical tools that provide a rigorous alternative to the powerful but heuristic replica methods from statistical physics.
- New methods for applications in sensing and communications where dense random matrices arise naturally from physical properties of the system. Examples include computational photography as well as compressive random access and massive-MIMO channel estimation in 5th-generation (5G) wireless communications.
- Robust algorithms for probabilistic inference of unknown matrices, including low-rank matrix factorization, robust PCA, blind deconvolution, self-calibration, and joint channel-symbol estimation.
- Theoretical understanding of problems in deep learning, including the fundamental limits of inference with deep generative models and information-theoretic bounds on the amount of data needed to train neural networks.