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Award Detail

Doing Business As Name:Ohio State University
  • Yingbin Liang
  • (609) 658-1330
Award Date:11/30/2017
Estimated Total Award Amount: $ 342,326
Funds Obligated to Date: $ 153,639
  • FY 2018=$77,883
  • FY 2017=$75,756
Start Date:10/01/2017
End Date:08/31/2021
Transaction Type:Grant
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.070
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:CIF: Medium: Collaborative Research: Nonconvex Optimization for High-Dimensional Signal Estimation: Theory and Fast Algorithms
Federal Award ID Number:1761506
DUNS ID:832127323
Parent DUNS ID:001964634
Program Officer:
  • Phillip Regalia
  • (703) 292-8910

Awardee Location

Street:Office of Sponsored Programs
Awardee Cong. District:03

Primary Place of Performance

Organization Name:Ohio State University
Street:Dreese Lab
Cong. District:03

Abstract at Time of Award

High-dimensional signal estimation plays fundamental roles in various engineering and science applications, such as medical imaging, video and network surveillance. Estimation procedures that maintain both statistical and computational efficacy are of great practical value, which translate into desiderata such as less time patients need to spend in a medical scanner, faster response to cyber attacks, and capabilities to handle very large datasets. While a lot of signal estimation tasks are naturally formulated as nonconvex optimization problems, existing results for nonconvex methods have several fundamental limitations, and the current state of the art is still limited in terms of when, why and which nonconvex approaches are effective for a given problem. The goal of this research program is to significantly deepen and broaden the understanding and applications of nonconvex optimization for high-dimensional signal estimation. In this project, the investigators will study high-dimensional signal estimation via direct optimization of nonconvex, and potentially nonsmooth, loss functions, without resorting to convex relaxation. This research will explore geometric structures shared by nonconvex functions commonly encountered in signal estimation, and study the fundamental roles these structures play in determining the algorithmic convergence. These results will then be exploited as guidelines to develop fast and provably correct algorithms for estimating high-dimensional signals with physically induced structures and under streaming data observations. Specifically, the research program consists of three major thrusts: (1) understanding the geometric structures of important classes of nonconvex loss surfaces, and characterizing their impact on the convergence of optimization algorithms; (2) developing fast algorithms and the associated theory for the recovery of structured low-rank matrices; (3) designing new online algorithms that are time and space efficient under a streaming setting, with the capability of detecting and tracking the time-varying signals of interest.

Publications Produced as a Result of this Research

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Y. Zhou, Y. Liang "Critical points of linear neural networks: Analytical forms and landscape properties" Proc. Sixth International Conference on Learning Representations (ICLR), v., 2018, p.. Citation details  

H. Zhang, Y. Liang "A nonconvex approach for phase retrieval: Reshaped Wirtinger flow and incremental algorithms" Journal of machine learning research, v.18, 2017, p.. Citation details  

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