论文标题
投影预测性推断广义线性和添加剂多级模型
Projection Predictive Inference for Generalized Linear and Additive Multilevel Models
论文作者
论文摘要
投影预测推断是一种决策理论贝叶斯方法，它将模型估计与决策做出分解。给定一个先前构建的参考模型，包括数据中存在的所有变量，投影预测性推理将其后部验到变量子集的受约束空间。然后，通过依次添加相关变量直到预测性能令人满意来执行变量选择。以前，仅针对广义线性模型（GLM）和高斯过程（GPS）证明了投影预测性推断，在该过程中，它表现出与竞争性变量选择程序相比的性能优越。在这项工作中，我们将投影预测推断扩展到支持通用线性多级模型（GLMM）和广义添加剂多级模型（GAMM）的变量和结构选择。我们的模拟和现实词实验表明，我们的方法可以大大降低达到参考预测性能并实现良好频率特性所需的模型复杂性。
Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive inference projects its posterior onto a constrained space of a subset of variables. Variable selection is then performed by sequentially adding relevant variables until predictive performance is satisfactory. Previously, projection predictive inference has been demonstrated only for generalized linear models (GLMs) and Gaussian processes (GPs) where it showed superior performance to competing variable selection procedures. In this work, we extend projection predictive inference to support variable and structure selection for generalized linear multilevel models (GLMMs) and generalized additive multilevel models (GAMMs). Our simulative and real-word experiments demonstrate that our method can drastically reduce the model complexity required to reach reference predictive performance and achieve good frequency properties.
