Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models
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稀疏超高维加性模型中的非参数独立筛选
- 研究问题
- 当变量的边际关系具有非线性、简单相关筛选可能不足时，如何在稀疏超高维加性模型中保留相关变量并降低维度？
- 方法与思路
- 作者将相关学习扩展为边际非参数学习，提出非参数独立筛选及相关方案，并以迭代版本改善加性模型拟合。
- 材料陈述的贡献
- 摘要称在技术条件下建立 sure screening 性质并量化降维程度，模拟和真实数据中表现优于所比较的方法。
- 阅读关注点
- 应核对边际信号与整体加性结构的关系、平滑复杂度、维度增长条件，以及迭代筛选的停止规则和比较方法设置。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列所谓温和条件或比较数值，保留真变量也不等于最终选择完全正确。
原文摘要
A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening is called NIS, a specific member of the sure independence screening. Several closely related variable screening procedures are proposed. Under the nonparametric additive models, it is shown that under some mild technical conditions, the proposed independence screening methods enjoy a sure screening property. The extent to which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, an iterative nonparametric independence screening (INIS) is also proposed to enhance the finite sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.