Group Sparse Additive Models
Group Sparse Additive Models
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发表时间：
2012-06
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通讯作者：
Junming Yin;X. Chen;E. Xing
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作者：
Junming Yin;X. Chen;E. Xing
我们考虑非参数加性模型中稀疏变量的选择问题，利用协变量之间结构的先验知识来鼓励一组变量中的那些变量被联合选择。以前的工作要么研究参数设置中的组稀疏性（例如，组套索），或者在不利用结构信息的情况下解决非参数设置中的问题（例如，稀疏加性模型）。在本文中，我们提出了一种新的方法，称为组稀疏加性模型（GroupSpAM），它可以处理组稀疏加性模型。我们推广了Hilbert空间的101/102范数作为GroupSpAM中的稀疏诱导惩罚。此外，我们推导出一个新的阈值条件，以确定在组水平的功能稀疏，并提出了一个有效的块坐标下降算法来构建的估计。我们通过仿真证明，GroupSpAM大大优于竞争方法的支持恢复和预测精度的加法模型，并进行了比较实验上的真实的乳腺癌数据集。
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either study the group sparsity in the parametric setting (e.g., group lasso), or address the problem in the nonparametric setting without exploiting the structural information (e.g., sparse additive models). In this paper, we present a new method, called group sparse additive models (GroupSpAM), which can handle group sparsity in additive models. We generalize the ℓ1/ℓ2 norm to Hilbert spaces as the sparsity-inducing penalty in GroupSpAM. Moreover, we derive a novel thresholding condition for identifying the functional sparsity at the group level, and propose an efficient block coordinate descent algorithm for constructing the estimate. We demonstrate by simulation that GroupSpAM substantially outperforms the competing methods in terms of support recovery and prediction accuracy in additive models, and also conduct a comparative experiment on a real breast cancer dataset.