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ESE Spring Seminar – “Solving Inverse Problems with Generative Priors: From Low-rank to Diffusion Models”

April 10 at 1:30 PM - 2:30 PM

: Generative priors are effective countermeasures to combat the curse of dimensionality, and enable efficient learning and inversion that otherwise are ill-posed, in data science. This talk begins with the classical low-rank prior, and introduces scaled gradient descent (ScaledGD), a simple iterative approach to directly recover the low-rank factors for a wide range of matrix and tensor estimation tasks. ScaledGD provably converges linearly at a constant rate independent of the condition number at near-optimal sample complexities, while maintaining the low per-iteration cost of vanilla gradient descent, even when the rank is overspecified and the initialization is random. Going beyond low rank, the talk discusses diffusion models as an expressive data prior in inverse problems, and introduces a plug-and-play posterior sampling method (Diffusion PnP) that alternatively calls two samplers, a proximal consistency sampler solely based on the forward model, and a denoising diffusion sampler solely based on the score functions of data prior. Performance guarantees and numerical examples will be demonstrated to illustrate the promise.

Yuejie Chi

Sense of Wonder Group Endowed Professor of Electrical and Computer Engineering in AI Systems, Canregie Mellow University

Dr. Yuejie Chi is the Sense of Wonder Group Endowed Professor of Electrical and Computer Engineering in AI Systems at Carnegie Mellon University, with courtesy appointments in the Machine Learning department and CyLab. She received her Ph.D. and M.A. from Princeton University, and B. Eng. (Hon.) from Tsinghua University, all in Electrical Engineering. Her research interests lie in the theoretical and algorithmic foundations of data science, signal processing, machine learning and inverse problems, with applications in sensing, imaging, decision making, and generative AI. Among others, Dr. Chi is a recipient of the Presidential Early Career Award for Scientists and Engineers (PECASE), the inaugural IEEE Signal Processing Society Early Career Technical Achievement Award for contributions to high-dimensional structured signal processing, and multiple paper awards including the SIAM Activity Group on Imaging Science Best Paper Prize and IEEE Signal Processing Society Young Author Best Paper Award. She is an IEEE Fellow (Class of 2023) for contributions to statistical signal processing with low-dimensional structures.


April 10
1:30 PM - 2:30 PM
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Electrical and Systems Engineering
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Towne 337