Theoretical properties of the overlapping groups lasso
Theoretical properties of the overlapping groups lasso
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DOI：
10.1214/12-ejs672
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发表时间：
2012-01-01
影响因子：
1.1
通讯作者：
Percival, Daniel
中科院分区：
文献类型：
--
作者：
Percival, Daniel
在线性回归的情况下，我们给出了Jacob，Obozinski和Vert(2009)关于重叠套索的两组理论结果。该方法在稀疏回归中联合选择预测器，允许对编码为一组的预测器进行复杂结构的稀疏。这一灵活的框架表明，任意复杂的结构可以用一组复杂的组进行编码。我们的结果表明，这一策略为该过程带来了意想不到的理论结果。特别地，我们给出了两组结果：(1)预测和估计的有限样本界；(2)渐近分布和选择。这两组结果都显示了为该过程选择越来越复杂的组集的负面后果，以及当该组组不能恢复真正的稀疏模式时的结果。此外，这些结果还显示了有重叠组和无重叠组的分组套索操作的异同。我们的分析表明，尽管该程序比标准套索方法更具优势，但必须谨慎选择基团集--过于复杂的基团集将损害分析。
We present two sets of theoretical results on the grouped lasso with overlap due to Jacob, Obozinski and Vert (2009) in the linear regression setting. This method jointly selects predictors in sparse regression, allowing for complex structured sparsity over the predictors encoded as a set of groups. This flexible framework suggests that arbitrarily complex structures can be encoded with an intricate set of groups. Our results show that this strategy results in unexpected theoretical consequences for the procedure. In particular, we give two sets of results: (1) finite sample bounds on prediction and estimation, and (2) asymptotic distribution and selection. Both sets of results demonstrate negative consequences from choosing an increasingly complex set of groups for the procedure, as well for when the set of groups cannot recover the true sparsity pattern. Additionally, these results demonstrate the differences and similarities between the the grouped lasso procedure with and without overlapping groups. Our analysis shows that while the procedure enjoys advantages over the standard lasso, the set of groups must be chosen with caution - an overly complex set of groups will damage the analysis.