High dimensional structured estimation with noisy designs

T. Amir Asiaee, Soumyadeep Chaterjee, Arindam Banerjee

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Structured estimation methods, such as LASSO, 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. In real world problems, however, covariates are usually corrupted with noise and there have been efforts to generalize structured estimation method for noisy covariate setting. In this paper we first show that without any information about the noise in covariates, currently established techniques of bounding statistical error of estimation fail to provide consistency guarantees. However, when information about noise covariance is available or can be estimated, then we prove consistency guarantees for any norm regularizer, which is a more general result than the state of the art. Next, we investigate empirical performance of structured estimation, specifically LASSO, when covariates are noisy and empirically show that LASSO is not consistent or stable in the presence of additive noise. However, prediction performance improves quite substantially when the noise covariance is available for incorporating in the estimator.

Original languageEnglish (US)
Title of host publication16th SIAM International Conference on Data Mining 2016, SDM 2016
EditorsSanjay Chawla Venkatasubramanian, Wagner Meira
PublisherSociety for Industrial and Applied Mathematics Publications
Pages801-809
Number of pages9
ISBN (Electronic)9781510828117
StatePublished - 2016
Externally publishedYes
Event16th SIAM International Conference on Data Mining 2016, SDM 2016 - Miami, United States
Duration: May 5 2016May 7 2016

Publication series

Name16th SIAM International Conference on Data Mining 2016, SDM 2016

Other

Other16th SIAM International Conference on Data Mining 2016, SDM 2016
CountryUnited States
CityMiami
Period5/5/165/7/16

ASJC Scopus subject areas

  • Computer Science Applications
  • Software

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