Publication Date: 08/16/2015 03:49
Latest Update: 08/23/2015 10:04

High Dimensional Structured Estimation with Noisy Designs

 

Amir Asiaee

 

Computer Science PhD student at University of Minnesota

 

 

22August 2015, 11:00- 12:00 pm

BLDG#2, Room 211

 

 

                                                                                 

Abstract

 

Structured estimation methods, such as LASSO and Dantzig Selector, have received considerable attention in recent years and substantial progress has been made in extending such methods to general norms and non-Gaussian design matrices. However, if covariates are corrupted with noise, empirical results of the literature suggest that such structured estimation methods fail to achieve consistency.  Assuming known noise covariance and employing that in the estimator is the current method for having consistent estimation in noisy design scenario. We follow the literature and assume that an estimate of the noise covriance is available, and show that consistent estimation is possible with only constant factor additional samples. In this well-studied context we "simplify" the current involved “constraint estimators”, and show that simple Dantzig selector is consistent for any norm. Also we "extend" the current line of work of “regularized estimation” for noisy design with l_1 norm to general norms. Finally we take the first steps to show theoretically that why having an estimate of noise covariance in the estimator is inevitable.

 

About the speaker

 

 

Amir Asiaee is a Ph.D. student in computer science department of University of Minnesota. His research interest is machine learning and specifically high dimensional statistics and large scale optimization with application in social network analysis and climate science.