A Unified Robust Regression Model for Lasso-like Algorithms
A Unified Robust Regression Model for Lasso-like Algorithms
复制标题
类套索算法的统一鲁棒回归模型
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Huan Xu
中科院分区：
文献类型：
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作者：
Wenzhuo Yang;Huan Xu
我们开发了一个统一的鲁棒线性回归模型，并证明了它相当于一个一般的正则化框架，以鼓励稀疏结构，其中包含组Lasso和融合Lasso作为具体的例子。这提供了一个鲁棒性的解释，这些广泛应用的Lasso算法，并允许我们通过考虑不同的不确定性集，构建新的泛化Lasso算法。使用这种鲁棒性的解释，我们提出了新的稀疏性结果，并建立统计一致性的建议正则化线性回归。这项工作扩展了Xu et al.（2010）的经典结果，该结果将具有鲁棒线性回归的标准Lasso与具有更一般稀疏结构的学习问题联系起来，并提供了新的基于鲁棒性的工具来理解具有稀疏结构的学习问题。
We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering different uncertainty sets. Using this robustness interpretation, we present new sparsity results, and establish the statistical consistency of the proposed regularized linear regression. This work extends a classical result from Xu et al. (2010) that relates standard Lasso with robust linear regression to learning problems with more general sparse-like structures, and provides new robustness-based tools to to understand learning problems with sparse-like structures.