论文标题
超高维广义添加剂模型：统一理论和方法
Ultra high dimensional generalized additive model: Unified Theory and Methods
论文作者
论文摘要
广义加性模型是一种强大的统计学习和预测建模工具，已在广泛的应用中应用。在处理诸如遗传数据分析之类的高贯穿数据的背景下，高维添加剂建模的需求是显着的。在本文中，我们研究了超高维广义添加剂模型的两步选择和估计方法。第一步将套索应用于函数的扩展基础上。有了很高的概率，这将选择所有非零函数，而不会过多选择。第二步使用自适应组拉索与任何初始估计器，包括满足某些规则条件的组套索估计器。自适应组套索估计量显示出与提高的收敛速率一致的选择。还讨论了调整参数选择并显示以在GIC程序下始终如一地选择真实模型。广泛的数值研究支持了理论特性。
Generalized additive model is a powerful statistical learning and predictive modeling tool that has been applied in a wide range of applications. The need of high-dimensional additive modeling is eminent in the context of dealing with high through-put data such as genetic data analysis. In this article, we studied a two step selection and estimation method for ultra high dimensional generalized additive models. The first step applies group lasso on the expanded bases of the functions. With high probability this selects all nonzero functions without having too much over selection. The second step uses adaptive group lasso with any initial estimators, including the group lasso estimator, that satisfies some regular conditions. The adaptive group lasso estimator is shown to be selection consistent with improved convergence rates. Tuning parameter selection is also discussed and shown to select the true model consistently under GIC procedure. The theoretical properties are supported by extensive numerical study.
