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Rank-based Lasso -- efficient methods for high-dimensional robust model selection
Methodology · Submitted 14 May 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Theoretical results are supported by the simulation study and the real data analysis, which show that our methods can properly identify relevant predictors, even when the error terms come from the Cauchy distribution and the link function is nonlinear.
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The abstract, sentence by sentence
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the unknown distribution. We utilize the natural, robust and efficient approach, which relies on replacing values of the response variables by their ranks and then identifying significant predictors by using well known Lasso. We provide new consistency results for the proposed procedure (called ,,RankLasso") and extend the scope of its applications by proposing its thresholded and adaptive versions. Our theoretical results show that these modifications can identify the set of relevant predictors under much wider range of data generating scenarios than regular RankLasso. Theoretical results are supported by the simulation study and the real data analysis, which show that our methods can properly identify relevant predictors, even when the error terms come from the Cauchy distribution and the link function is nonlinear. They also demonstrate the superiority of the modified versions of RankLasso in the case when predictors are substantially correlated. The numerical study shows also that RankLasso performs substantially better in model selection than LADLasso, which is a well established methodology for robust model selection.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the unknown distribution. | background 1.00 | 0.11 | 0.03 | asserted 0.93 |
| s1 | We utilize the natural, robust and efficient approach, which relies on replacing values of the response variables by their ranks and then identifying significant predictors by using well known Lasso. | method 0.98 | 0.79 | 0.07 | asserted 0.99 |
| s2 | We provide new consistency results for the proposed procedure (called ,,RankLasso") and extend the scope of its applications by proposing its thresholded and adaptive versions. | contribution 1.00 | 0.94 | 0.15 | asserted 1.00 |
| s3 | Our theoretical results show that these modifications can identify the set of relevant predictors under much wider range of data generating scenarios than regular RankLasso. | result 0.88 | 0.92 | 0.38 | asserted 1.00 |
| s4 | Theoretical results are supported by the simulation study and the real data analysis, which show that our methods can properly identify relevant predictors, even when the error terms come from the Cauchy distribution and the link function is nonlinear. | result 0.98 | 0.95 | 0.30 | asserted 1.00 |
| s5 | They also demonstrate the superiority of the modified versions of RankLasso in the case when predictors are substantially correlated. | result 0.99 | 0.91 | 0.12 | asserted 1.00 |
| s6 | The numerical study shows also that RankLasso performs substantially better in model selection than LADLasso, which is a well established methodology for robust model selection. | result 1.00 | 0.94 | 0.20 | asserted 1.00 |
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The paper
Original abstract
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the unknown distribution. We utilize the natural, robust and efficient approach, which relies on replacing values of the response variables by their ranks and then identifying significant predictors by using well known Lasso. We provide new consistency results for the proposed procedure (called ,,RankLasso") and extend the scope of its applications by proposing its thresholded and adaptive versions. Our theoretical results show that these modifications can identify the set of relevant predictors under much wider range of data generating scenarios than regular RankLasso. Theoretical results are supported by the simulation study and the real data analysis, which show that our methods can properly identify relevant predictors, even when the error terms come from the Cauchy distribution and the link function is nonlinear. They also demonstrate the superiority of the modified versions of RankLasso in the case when predictors are substantially correlated. The numerical study shows also that RankLasso performs substantially better in model selection than LADLasso, which is a well established methodology for robust model selection.
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How the literature uses it
1 arXiv paper cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 1 paper
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Following [ref] we preprocess the data by removing probes for which the maximum expression level among the 210 individuals is smaller than the 25-th percentile of all measured expression levels and for which the range of expression levels among the 210 individuals is smaller than 2.
Identifying important predictors in large data bases -- multiple testing and model selection · Continous response · 0.97
What it cites · 1 sentence without a confident label
Uses the method or tool of 1 paper
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In Table [ref] we compare the average times needed to invoke RankLasso using the glmnet package [ref] in the R software [ref] and the robust LADLasso using the R package MTE [ref] .
Penalized Maximum Tangent Likelihood Estimation and Robust Variable Selection · Simulation study · 0.92
Cites as background 1 paper
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The properties of Lasso in model selection, estimation and prediction are deeply investigated, e.g. in [ref] .
On the sign recovery by LASSO, thresholded LASSO and thresholded Basis Pursuit Denoising · Introduction · 0.96
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