Electronic Journal of Statistics

Quantile universal threshold

Caroline Giacobino, Sylvain Sardy, Jairo Diaz-Rodriguez, and Nick Hengartner

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Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to zero, estimators such as lasso, elastic net and subset selection perform variable selection. One crucial step challenges all these estimators: the amount of thresholding governed by a threshold parameter $\lambda $. If too large, important features are missing; if too small, incorrect features are included. Within a unified framework, we propose a selection of $\lambda $ at the detection edge. To that aim, we introduce the concept of a zero-thresholding function and a null-thresholding statistic, that we explicitly derive for a large class of estimators. The new approach has the great advantage of transforming the selection of $\lambda $ from an unknown scale to a probabilistic scale. Numerical results show the effectiveness of our approach in terms of model selection and prediction.

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Electron. J. Statist. Volume 11, Number 2 (2017), 4701-4722.

Received: March 2017
First available in Project Euclid: 24 November 2017

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Convex optimization high-dimensionality sparsity regularization thresholding

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Giacobino, Caroline; Sardy, Sylvain; Diaz-Rodriguez, Jairo; Hengartner, Nick. Quantile universal threshold. Electron. J. Statist. 11 (2017), no. 2, 4701--4722. doi:10.1214/17-EJS1366. https://projecteuclid.org/euclid.ejs/1511492459

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