Electronic Journal of Statistics

Recovery of weak signal in high dimensional linear regression by data perturbation

Yongli Zhang

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How to recover weak signals (i.e., small nonzero regression coefficients) is a difficult task in high dimensional feature selection problems. Both convex and nonconvex regularization methods fail to fully recover the true model whenever there exist strong columnwise correlations in design matrices or small nonzero coefficients below some threshold. To address the two challenges, we propose a procedure, Perturbed LASSO (PLA), that weakens correlations in the design matrix and strengthens signals by adding random perturbations to the design matrix. Moreover, a quantitative relationship between the selection accuracy and computing cost of PLA is derived. We theoretically prove and demonstrate using simulations that PLA substantially improves the chance of recovering weak signals and outperforms comparable methods at a limited cost of computation.

Article information

Electron. J. Statist. Volume 11, Number 2 (2017), 3226-3250.

Received: November 2016
First available in Project Euclid: 25 September 2017

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Zentralblatt MATH identifier

Primary: 62J07: Ridge regression; shrinkage estimators

Beta-min condition data perturbation high dimensional data irrepresentable condition LASSO weak signal

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Zhang, Yongli. Recovery of weak signal in high dimensional linear regression by data perturbation. Electron. J. Statist. 11 (2017), no. 2, 3226--3250. doi:10.1214/17-EJS1320. https://projecteuclid.org/euclid.ejs/1506326416

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