Iteratively reweighted ℓ1-penalized robust regression
Iteratively reweighted ℓ1-penalized robust regression
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DOI：
10.1214/21-ejs1862
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发表时间：
2021-01
影响因子：
1.1
通讯作者：
Xiaoou Pan;Qiang Sun;Wen-Xin Zhou
中科院分区：
文献类型：
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作者：
Xiaoou Pan;Qiang Sun;Wen-Xin Zhou
本文研究了具有非凸正则化的高维鲁棒回归的优化误差、统计收敛率和重尾误差影响之间的权衡。当线性模型中的加性误差只有有界的秒矩时，我们证明了在弱β -min条件下，迭代重加权1惩罚自适应Huber回归估计器满足指数偏差界和oracle性质，包括oracle收敛率和变量选择一致性。在计算上，我们需要多达O（log s + log log d）次迭代才能得到这样一个oracle估计器，其中s和d分别表示稀疏性和环境维数。同时考虑了对一般鲁棒损失函数的推广。数值研究为我们的方法和理论提供了有力的支持。MSC2020学科分类：Primary 62A01；二次62 j07。
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moments, we show that iteratively reweighted 1-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition. Computationally, we need as many as O(log s + log log d) iterations to reach such an oracle estimator, where s and d denote the sparsity and ambient dimension, respectively. Extension to a general class of robust loss functions is also considered. Numerical studies lend strong support to our methodology and theory. MSC2020 subject classifications: Primary 62A01; secondary 62J07.