Sparse additive models
Sparse additive models
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DOI：
10.1111/j.1467-9868.2009.00718.x
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发表时间：
2009-01-01
影响因子：
5.8
通讯作者：
Wasserman, Larry
中科院分区：
文献类型：
--
作者：
Ravikumar, Pradeep;Lafferty, John;Wasserman, Larry
我们提出了一类新的高维非参数回归和分类方法，称为稀疏加性模型。我们的方法结合了稀疏线性建模和加性非参数回归的思想。我们推导出一种即使在协变量数量大于样本大小时也实用且有效的模型拟合算法。稀疏加法模型本质上是 Yuan 和 Lin 分组套索的函数版本。它们也与 Lin 和Zhang 的 COSSO 模型密切相关，但将平滑和稀疏性解耦，从而可以使用任意非参数平滑器。我们分析了稀疏加性模型的理论特性，并给出了合成数据和真实数据的实证结果，表明它们可以有效地拟合高维数据中的稀疏非参数模型。
We present a new class of methods for high dimensional non-parametric regression and classification called sparse additive models. Our methods combine ideas from sparse linear modelling and additive non-parametric regression. We derive an algorithm for fitting the models that is practical and effective even when the number of covariates is larger than the sample size. Sparse additive models are essentially a functional version of the grouped lasso of Yuan and Lin. They are also closely related to the COSSO model of Lin and Zhang but decouple smoothing and sparsity, enabling the use of arbitrary non-parametric smoothers. We give an analysis of the theoretical properties of sparse additive models and present empirical results on synthetic and real data, showing that they can be effective in fitting sparse non-parametric models in high dimensional data.