Nonconvex Low-Rank Matrix Estimation: Geometry, Robustness, and Acceleration is coming at 04/16/2020 - 4:00pm
via Zoom Thu, 04/16/2020 - 4:00pm Yuejie Chi Assoc. Prof., Carnegie Mellon University Abstract: Many inverse problems encountered in sensing and imaging can be formulated as estimating a low-rank matrix from incomplete linear measurements; examples include phase retrieval, matrix completion, blind deconvolution, and so on. Through the lens of matrix factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent to recover the low-rank factors directly, which allow a small memory footprint. Despite wide empirical success, the theoretical underpinnings have remained elusive. In this talk, I will discuss our recent line of efforts in understanding the geometry of the nonconvex loss landscape with the aid of statistical reasoning, and how gradient descent harnesses such geometry in an implicit manner to achieve both computational and statistical efficiency all at once. Furthermore, I will discuss how to adjust vanilla gradient descent to make it provably robust to outliers and ill-conditioning without losing computational and statistical efficiency for low-rank matrix sensing. Bio: Read more: https://eecs.oregonstate.edu/colloquium/nonconvex-low-rank-matrix-estima... [1] [1] https://eecs.oregonstate.edu/colloquium/nonconvex-low-rank-matrix-estimation-geometry-robustness-and-acceleration
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