l1 Regularization in Infinite Dimensional Feature Spaces
l1 Regularization in Infinite Dimensional Feature Spaces
复制标题
l1 无限维特征空间中的正则化
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Ji Zhu
中科院分区：
文献类型：
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作者：
Saharon Rosset;G. Swirszcz;N. Srebro;Ji Zhu
在本文中，我们讨论的问题拟合l1正则化预测模型在无限（可能是不可数）维特征空间。我们的主要贡献是：a。基于可以应用于非可数特征空间的度量导出l1正则化的推广; B.证明了l1正则化的稀疏性在无限维中保持不变; c.设计一种路径跟踪算法，该算法可以在“nice”特征空间中生成正则化解的集合;以及d.给出了一个惩罚样条模型的例子，其中该路径跟踪算法在计算上是可行的，并给出了令人鼓舞的实证结果。
In this paper we discuss the problem of fitting l1 regularized prediction models in infinite (possibly non-countable) dimensional feature spaces. Our main contributions are: a. Deriving a generalization of l1 regularization based on measures which can be applied in non-countable feature spaces; b. Proving that the sparsity property of l1 regularization is maintained in infinite dimensions; c. Devising a path-following algorithm that can generate the set of regularized solutions in "nice" feature spaces; and d. Presenting an example of penalized spline models where this path following algorithm is computationally feasible, and gives encouraging empirical results.