High dimensional structured additive regression models: Bayesian regularization, smoothing and predictive performance
High dimensional structured additive regression models: Bayesian regularization, smoothing and predictive performance
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DOI：
10.1111/j.1467-9876.2010.00723.x
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发表时间：
2011-01-01
影响因子：
1.6
通讯作者：
Fahrmeir, Ludwig
中科院分区：
文献类型：
--
作者：
Kneib, Thomas;Konrath, Susanne;Fahrmeir, Ludwig
现代应用中的数据结构经常联合收割机结合灵活的回归技术处理的必要性，例如，具有高维协变量向量的非线性和空间效应。而前者的估计通常是通过补充一个合适的平滑惩罚的可能性，后者通常被分配收缩惩罚，强制稀疏模型。我们认为贝叶斯统一的角度来看，条件高斯先验可以分配给所有类型的回归效应。对高斯分布的方差进行适当的超先验假设，然后诱导出所需的平滑性或稀疏性。作为一个主要的优点，一般的马尔可夫链蒙特卡罗模拟算法可以开发，允许联合估计的平滑和空间的影响和正则化的系数向量。两个应用程序证明了所提出的程序的实用性：从租赁指南在慕尼黑和添加剂的概率模型的预测消费信贷违约的数据的地理添加剂回归模型。在这两种情况下，分类协变量的高维向量将被纳入回归模型。与专家模型相比，所得到的高维结构化加法回归模型的预测能力是特别相关的，并将在交叉验证测试数据上进行评估。
Data structures in modern applications frequently combine the necessity of flexible regression techniques handling, for example, non-linear and spatial effects with high dimensional covariate vectors. Whereas estimation of the former is typically achieved by supplementing the likelihood with a suitable smoothness penalty, the latter are usually assigned shrinkage penalties that enforce sparse models. We consider a Bayesian unifying perspective, where conditionally Gaussian priors can be assigned to all types of regression effects. Suitable hyperprior assumptions on the variances of the Gaussian distributions then induce the desired smoothness or sparseness properties. As a major advantage, general Markov chain Monte Carlo simulation algorithms can be developed that allow for the joint estimation of smooth and spatial effects and regularized coefficient vectors. Two applications demonstrate the usefulness of the procedure proposed: a geoadditive regression model for data from a rental guide in Munich and an additive probit model for the prediction of consumer credit defaults. In both cases, high dimensional vectors of categorical covariates will be included in the regression models. The predictive ability of the resulting high dimensional structured additive regression models compared with expert models is of particular relevance and will be evaluated on cross-validation test data.