TY - GEN
T1 - High dimensional structured estimation with noisy designs
AU - Amir Asiaee, T.
AU - Chaterjee, Soumyadeep
AU - Banerjee, Arindam
N1 - Publisher Copyright:
Copyright © by SIAM.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:84991677285
T3 - 16th SIAM International Conference on Data Mining 2016, SDM 2016
SP - 801
EP - 809
BT - 16th SIAM International Conference on Data Mining 2016, SDM 2016
A2 - Venkatasubramanian, Sanjay Chawla
A2 - Meira, Wagner
PB - Society for Industrial and Applied Mathematics Publications
T2 - 16th SIAM International Conference on Data Mining 2016, SDM 2016
Y2 - 5 May 2016 through 7 May 2016
ER -