Fundamental Limits and Efficient Algorithms for Tensor Inverse Problems
Abstract
The main themes of this proposal address multiple timely and important problems related to theoretical foundations for tensor big da"ta. Given the ubiquitousness of multi-perspective, multi-dimensional big data in our day-to-day lives, new models, theories and algo"rithms to enhance our fundamentalunderstanding of such data and to enable us to efficiently process them are of significant importance. This proposal directly addresses these issues by bringing a fresh and novel set of tools and ideas which can be of immense util"ity in advancing the big data science and engineering. Impacted fields includelarge-scale data analysis, recommendation systems and"" personalization, neural signal analysis, and communication and signal processing. This proposal addresses the fundamental limits, n"ovel optimization formulations and development of provably efficient algorithms for tensor completion and other tensor inverse problems. It consists of the following four research thrusts. (1) We propose to derive deterministic and probabilistic conditions for low#NAME?d. (2) We propose to apply the atomic norm minimization framework to infer low-rank tensors using structure promoting convex optimiz"ations. (3) We propose to reformulate the atomic norm regularized convex programs into nonconvex ones with smaller memory footprint,"" resulting in low-complexity algorithms that are more scalable and efficient, with provable global optimality. (4) We propose to dev"elop transform-domain tensor models and extend tensor completion theories and algorithms for such models. We expect that the project" will not only produce novel algorithms and methodologies for tensor big-data models, but also apply these newer approaches to real" data from open-source databases. The proposed project willlay out theoretical and computational foundations for big tensor inverse problems by investigating the fundamental limits and convex and nonconvex geometries of tensor optimizations. The ability to scale these optimizations to big data applications with optimal performance and guaranteed convergence willensure the research has the broadest possible impact.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 01, 2017
- Source ID
- N000141712827
Entities
People
- Xiaodong Wang
Organizations
- Office of Naval Research
- Trustees of Columbia University in the City of New York
- United States Navy