The BerHu penalty and the grouped effect
By Laurent Zwald, Sophie Lambert-Lacroix. 2012
92 citations recorded by the source corpus.
The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size and large covariables numbers, this penalty is not very satisfactory variable selection method. In this paper, we introduce an adaptive reversed version of Huber's criterion as a penalty function. We call this penalty adaptive Berhu penalty. As for elastic net penalty, small coefficients contribute their $\ell_1$ norm to this penalty while larger coefficients cause it to grow quadratically (as ridge regression). We show that the estimator associated with criterion such that ordinary least square or Huber's one combining with adaptive Berhu penalty enjoys the oracle properties. In addition, this procedure encourages a grouping effect. This approach is compared with adaptive elastic net regularization. Extensive simulation studies demonstrate satisfactory finite-sample performance of such procedure. A real example is analyzed for illustration purposes. Keywords : Adaptive Berhu penalty; concomitant scale; elastic net penalty; Huber's criterion; oracle property; robust estimation.
Subfields: Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a4fea0f09f764b5791221be203f7d8810ab11ecb
How researchers see this paper
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In Control and Systems Engineering
In Statistics and Probability
- Nassir Navab
- Ping Tan
- Vasileios Belagiannis
- Federico Tombari
- Chengzhou Tang
- Iro Laina
- Christian Rupprecht
Citations in the corpus
- Deeper Depth Prediction with Fully Convolutional Residual Networks (2016, methodology): “Although this produces good results in our test cases, we found that using the reverse Huber (berHu) [25, 40] as loss function B yields a better final error than L2.”
- Monocular depth estimation based on deep learning: An overview (2020, methodology): “During the training process, they use the reverse Huber (Berhu) [55] as the supervised signal”
- BA-Net: Dense Bundle Adjustment Network (2018, methodology): “Depth Map Loss For each dense depth map we applies the berHu Loss (Zwald & Lambert-Lacroix, 2012) as in Laina et al. (2016).”