Rigorous Modeling and Computation for Sparse Multivariate Statistical Problems
Abstract
which comes in diverse forms from engineering, scientific, social and industrial ``big?data" applications. In the modern day ``high dimensional setting a lot of exciting research is being conducted in learning sparse, parsimonious and interpretable models. The research problems studied in this project will contribute to our understanding of concepts fundamental to these tasks. The work broadly encompasses developing statistical models for these tasks, understanding their methodological properties and building efficient algorithms for them. Emphasis will be placed in providing new perspectives for most of these problems. A main theme in this research pursuit is the cross?fertilization of ideas across the disciplines of statistics, mathematical optimization and numerical linear algebra. The investigation aims to systematically understand statistical methods and their properties with the aid of such interdisciplinary tools. The proposed research project has three major parts. The first part explores a new paradigm in statistical estimation problems???the use of Mixed Integer Optimization. The second part addresses a few important problems in modeling and computation for learning with low?rank matrices. The third part studies boosting methods in linear regression via a new perspective that will lead to a new rigorous understanding of data?fidelity vis?à?vis shrinkage bounds for a class of boosting methods. A successful execution of the project will (a) enhance the state?of?art in rigorous statistical modeling for complex tasks using tractable computational procedures; and (b) strengthen our methodological understanding of statistical techniques that play a fundamental role in these tasks. 1
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512342
Entities
People
- Rahul Mazumder
Organizations
- Massachusetts Institute of Technology
- Office of Naval Research
- United States Navy