Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection
Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection
复制标题
DOI：
10.1007/s11222-009-9158-3
复制
发表时间：
2010-04-01
影响因子：
2.2
通讯作者：
Konrath, Susanne
中科院分区：
文献类型：
--
作者：
Fahrmeir, Ludwig;Kneib, Thomas;Konrath, Susanne
本文从统一的角度调查了各种收缩、平滑和选择先验，并展示了如何将它们组合起来，以在一般类型的结构化加性回归模型中进行贝叶斯正则化。作为一个共同特征，所有正则化先验都是条件高斯分布，给定进一步正则化模型复杂性的参数。这些参数的超先验鼓励收缩、平滑或选择。结果表明，这些正则化（对数）先验可以解释为几个著名的频率论惩罚项的贝叶斯类似物。可以使用统一且计算高效的 MCMC 方案进行推理，同时估计正则化回归系数和基函数系数以及复杂性参数，并通过相应的边缘后验测量不确定性。对于变量和函数选择，我们讨论了尖峰和平板先验的几种变体，它们也可以放入条件高斯先验的框架中。贝叶斯正则化方法的性能在危险回归模型和高维地理可加回归模型中得到了证明。
This paper surveys various shrinkage, smoothing and selection priors from a unifying perspective and shows how to combine them for Bayesian regularisation in the general class of structured additive regression models. As a common feature, all regularisation priors are conditionally Gaussian, given further parameters regularising model complexity. Hyperpriors for these parameters encourage shrinkage, smoothness or selection. It is shown that these regularisation (log-) priors can be interpreted as Bayesian analogues of several well-known frequentist penalty terms. Inference can be carried out with unified and computationally efficient MCMC schemes, estimating regularised regression coefficients and basis function coefficients simultaneously with complexity parameters and measuring uncertainty via corresponding marginal posteriors. For variable and function selection we discuss several variants of spike and slab priors which can also be cast into the framework of conditionally Gaussian priors. The performance of the Bayesian regularisation approaches is demonstrated in a hazard regression model and a high-dimensional geoadditive regression model.