Safe feature screening rules for the regularized Huber regression

Chen, Huangyue; Kong, Lingchen; Shang, Pan; Pan, Shuxiang

doi:10.1016/j.amc.2020.125500

Cited by 8 publications

(2 citation statements)

References 21 publications

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“…(i) Let β * (λ) = 0. By Theorem 3.1 and the KKT system (5), we know that y = α, θ * (λ) ∈ F and λ ≥ X T θ max ∞ with any θ max ∈ F defined in (6). Because F is a set, λ needs to satisfy that λ ≥ max…”

Section: Theorem 31 (Strong Duality Theorem)mentioning

confidence: 99%

“…For robust loss functions, there are a few screening rules. For instance, Chen et al [6] proposed the safe screening rules for the regularized Huber regression. To the best of our knowledge, existing screening rules mainly focus on regularized models with differentiable loss functions, such as the quadratic function, logistic function and Huber function.…”

Section: Introductionmentioning

confidence: 99%

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l1-norm quantile regression screening rule via the dual circumscribed sphere

Shang¹,

Kong²

2020

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1 -norm quantile regression is a common choice if there exists outlier or heavy-tailed error in high-dimensional data sets. However, it is computationally expensive to solve this problem when the feature size of data is ultra high. As far as we know, existing screening rules can not speed up the computation of the 1 -norm quantile regression, which dues to the non-differentiability of the quantile function/pinball loss. In this paper, we introduce the dual circumscribed sphere technique and propose a novel 1 -norm quantile regression screening rule. Our rule is expressed as the closed-form function of given data and eliminates inactive features with a low computational cost. Numerical experiments on some simulation and real data sets show that this screening rule can be used to eliminate almost all inactive features. Moreover, this rule can help to reduce up to 23 times of computational time, compared with the computation without our screening rule.

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Section: Theorem 31 (Strong Duality Theorem)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%