This talk describes the Alternating Gradient Descent (GD) and Minimization (AltGDmin) algorithm which provides a faster and more communication-efficient solution for many optimization problems for which Alternating Minimization (AltMin) is a popular solution. Consider the class of problems in which the set of optimization variables, Z, can be split into two parts. AltGDmin is more efficient than both AltMin and GD for any problem for which (i) the minimization over one set of variables is much quicker than that over the other set; and (ii) the cost function is differentiable w.r.t. the latter. Often, the reason for (i) is that the problem is at least partly “decoupled” and each of the decoupled problems is quick to solve. Important examples of partly decoupled problems include low rank column-wise matrix sensing (LRCS), low rank matrix completion (LRMC), data clustering, and unlabeled sensing. LRCS is a lesser known LR recovery problem that finds applications in multi-task representation learning, few-shot learning and dynamic MRI.

AltGDmin was introduced in our recent work as a provably fast, communication-efficient, and sample-efficient GD-based approach for solving the LRCS problem. In ongoing work, we have also obtained sample and iteration complexity guarantees for AltGDmin for solving the LRMC problem and argued that it is sample- and communication-efficient. We also demonstrate the advantage (speed and generality) of AltGDmin over the existing state-of-the-art for LRCS-based compressive dynamic MRI.

Bio:

Namrata Vaswani received a Ph.D. from the University of Maryland College Park (UMD) in 2004 and a B.Tech from IIT-Delhi in India in 1999. Since Fall 2005, she has been with the Iowa State University where she is currently the Anderlik Professor of Electrical and Computer Engineering. Her research interests lie in data science, with a particular focus on Statistical Machine Learning and Signal Processing. She also directs the CyMath (graduate student led K-8 Math tutoring) program at Iowa State. Vaswani has served as an Associate Editor, Area Editor or Guest Editor for IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing, the Signal Processing Magazine and Proceedings of the IEEE.

She is a recipient of the 2014 IEEE Signal Processing Society Best Paper Award, the UMD ECE Distinguished Alumni Award (2019) and the Iowa State Mid-Career Achievement in Research Award (2019). Vaswani is an AAAS Fellow (class of 2023) and an IEEE Fellow (class of 2019).

### Recorded Talk

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