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Title: Nonconvex Optimization Meets Low-Rank Matrix Factorization
Date: 17 May 2022
Time: 10:30 AM ET (New York time)
Duration: Approximately 1 Hour
Presenters: Dr. Yuejie Chi
Based on the IEEE Xplore® article: Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
Published: IEEE Transactions on Signal Processing, August 2019
Download: Original article will be made freely available for download for 48 hours from the day of the webinar, on IEEE Xplore®
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: 1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and 2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, and robust principal component analysis. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.
Yuejie Chi (S'09-M'12-SM'17) received the B.E. (Hon.) degree in electrical engineering from Tsinghua University, Beijing, China, in 2007, and the M.A. and Ph.D. degrees in electrical engineering from Princeton University, Princeton, NJ, in 2009 and 2012, respectively.
From 2012 to 2017, she was with the Ohio State University, and since 2018, she has been with the Department of Electrical and Computer Engineering at Carnegie Mellon University, where she is now a professor with courtesy appointments in the Machine Learning Department and CyLab. At Carnegie Mellon, she held the inaugural Robert E. Doherty Early Career Development Professorship from 2018 to 2020. Her research interests lie in the theoretical and algorithmic foundations of data science, signal processing, machine learning and inverse problems, with applications in sensing and societal systems, broadly defined.
Dr. Chi is a recipient of 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, IEEE Signal Processing Society Young Author Best Paper Award. She was named a Goldsmith Lecturer by IEEE Information Theory Society, and a Distinguished Lecturer by IEEE Signal Processing Society. She currently serves as an Associate Editor for IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing, and IEEE Trans. on Pattern Recognition and Machine Intelligence.
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