新模型同时学习未知链接函数和变量交互，适合高维数据建模。
Generalized Sparse Additive Model with Unknown Link Function
- 用B样条和MLP分别估计分量函数与未知链接函数
- 通过ℓ₂,₁正则化实现变量选择与隐含交互发现
- 理论保证收敛性，实测在合成与真实数据上均有效
广义加性模型（GAM）已成功应用于高维数据分析。然而，现有方法难以同时估计链接函数、分量函数及变量交互。为此，本文提出一种新的稀疏加性模型——未知链接函数的广义稀疏加性模型（GSAMUL），其中分量函数采用B样条基估计，未知链接函数由多层感知机（MLP）网络建模，并引入ℓ₂,₁-范数正则化实现变量选择。该模型可同时完成变量选择与隐含交互识别。我们将估计过程整合为双层优化问题，将数据分为训练集与验证集。理论上，我们提供了近似算法的收敛性保证；在应用上，合成数据与真实数据集上的实验结果一致验证了该方法的有效性。
原文摘要 · Abstract (English)
Generalized additive models (GAM) have been successfully applied to high dimensional data analysis. However, most existing methods cannot simultaneously estimate the link function, the component functions and the variable interaction. To alleviate this problem, we propose a new sparse additive model, named generalized sparse additive model with unknown link function (GSAMUL), in which the component functions are estimated by B-spline basis and the unknown link function is estimated by a multi-layer perceptron (MLP) network. Furthermore, $\ell_{2,1}$-norm regularizer is used for variable selection. The proposed GSAMUL can realize both variable selection and hidden interaction. We integrate this estimation into a bilevel optimization problem, where the data is split into training set and validation set. In theory, we provide the guarantees about the convergence of the approximate procedure. In applications, experimental evaluations on both synthetic and real world data sets consistently validate the effectiveness of the proposed approach.
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