Research > Faculty Projects

NSF Career: Parsimonious Modeling via Matrix Rank Minimization

Principal Investigator
Maryam Fazel

Sponsor(s)
NSF

Award Period
09/16/2009 - 09/15/2014

Abstract
The goal of the research program proposed here is to provide a theoretical and computational foundation for systematically deriving a "parsimonious" or low-complexity model, given experimental data, observations, and prior information about the model.

In many engineering applications, notions such as order or complexity of a model can be expressed as the rank of an appropriate matrix, in which case choosing the simplest among all feasible models can be posed mathematically as a "rank minimization problem". A low-rank matrix could correspond to a low-order controller for a mechanical system, a low-degree statistical model for a random process, or an embedding of large data sets in a low- dimensional space. This project aims to propose fast, computationally efficient algorithms based on convex optimization for parsimonious modeling and matrix rank optimization, which is well known to be computationally hard. Based on preliminary results, it also aims to prove theoretical guarantees for the algorithms in certain cases. Applications arise in computer vision, machine learning, portfolio optimization, and signal processing.

Updates or corrections to this page should be sent to gheaton@u.washington.edu.