组选择与收缩：半参数可加模型的结构化稀疏性
Group selection and shrinkage: Structured sparsity for semiparametric additive models
AI总结：
针对统计与机器学习中的组结构稀疏问题，提出结合组子集选择与收缩、支持组任意重叠的结构化稀疏估计器，构建优化框架并给出误差界，在半参数可加建模等任务中表现更优，且提供grpsel开源实现。
摘要：
遵循组结构的稀疏回归与分类估计器可应用于各类统计与机器学习问题，涵盖多任务学习、稀疏可加建模到层级选择等场景。本文提出结合组子集选择与收缩的结构化稀疏估计器；为适配复杂结构，该估计器允许组间存在任意重叠。我们构建了用于拟合非凸正则化曲面的优化框架，并给出了回归函数估计的有限样本误差界。作为一类需要结构约束的应用场景，我们研究了稀疏半参数可加建模——该方法允许每个预测变量的效应为零、线性或非线性。针对该任务，新估计器在合成数据上的多项指标均优于对比方法。最后，我们验证了其在利用多预测变量建模超市客流量与经济衰退问题中的有效性。这些示例表明，采用新估计器拟合的稀疏半参数可加模型，是完全线性方法与完全非参数方法之间的极佳折中方案。所有算法均通过可扩展实现工具grpsel开放使用。
英文摘要：
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection. This work introduces structured sparse estimators that combine group subset selection with shrinkage. To accommodate sophisticated structures, our estimators allow for arbitrary overlap between groups. We develop an optimization framework for fitting the nonconvex regularization surface and present finite-sample error bounds for estimation of the regression function. As an application requiring structure, we study sparse semiparametric additive modeling, a procedure that allows the effect of each predictor to be zero, linear, or nonlinear. For this task, the new estimators improve across several metrics on synthetic data compared to alternatives. Finally, we demonstrate their efficacy in modeling supermarket foot traffic and economic recessions using many predictors. These demonstrations suggest sparse semiparametric additive models, fit using the new estimators, are an excellent compromise between fully linear and fully nonparametric alternatives. All of our algorithms are made available in the scalable implementation grpsel.
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