Selective Factor Extraction in High Dimensions
Selective Factor Extraction in High Dimensions
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DOI：
10.1093/biomet/asw059
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发表时间：
2014-03
期刊：
影响因子：
--
通讯作者：
Yiyuan She
中科院分区：
文献类型：
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作者：
Yiyuan She
本文研究监督和无监督学习中的同步特征选择和提取。我们提出并研究选择性降序回归，以从输入特征的简约子集中构建最佳解释因素。所提出的估计器享有尖锐的预言不等式，并且通过模型选择的预测信息标准，它们通过控制系数矩阵的秩和行支持来适应未知的稀疏性。开发了一类算法，可以适应各种凸和非凸稀疏性惩罚，并且可用于高维多元数据中的秩约束变量筛选。该论文还展示了宏观经济学和计算机视觉中的应用，以展示如何通过联合变量选择和投影来有效捕获低维数据结构。
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix. A class of algorithms is developed that can accommodate various convex and nonconvex sparsity-inducing penalties, and can be used for rank-constrained variable screening in high-dimensional multivariate data. The paper also showcases applications in macroeconomics and computer vision to demonstrate how low-dimensional data structures can be effectively captured by joint variable selection and projection.