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- W2799842021 abstract "The high-dimensional linear model $y = X beta^0 + epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $beta^0.$ We introduce Lasso-Zero, a new $ell_1$-based estimator whose novelty resides in an overfit, then paradigm and the use of noise dictionaries concatenated to $X$ for overfitting the response. To select the threshold, we employ the quantile universal threshold based on a pivotal statistic that requires neither knowledge nor preliminary estimation of the noise level. Numerical simulations show that Lasso-Zero performs well in terms of support recovery and provides an excellent trade-off between high true positive rate and low false discovery rate compared to competitors. Our methodology is supported by theoretical results showing that when no noise dictionary is used, Lasso-Zero recovers the signs of $beta^0$ under weaker conditions on $X$ and $S^0$ than the Lasso and achieves sign consistency for correlated Gaussian designs. The use of noise dictionary improves the procedure for low signals." @default.
- W2799842021 created "2018-05-17" @default.
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- W2799842021 date "2018-05-14" @default.
- W2799842021 modified "2023-10-01" @default.
- W2799842021 title "Model selection with lasso-zero: adding straw to the haystack to better find needles" @default.
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