论文标题
潜在的高斯模型留下组交叉验证
Leave-group-out cross-validation for latent Gaussian models
论文作者
论文摘要
通常使用交叉验证来评估统计模型的预测性能。在各种方法中，经常使用保留的交叉验证（LOOCV）。 LOOCV最初设计用于可交换的观测，此后已将其扩展到其他情况，例如分层模型。但是，它主要集中在短期预测上，并且可能无法完全捕获远程预测方案。对于结构化的层次模型，尤其是涉及多个随机效应的模型，短期和长期预测的概念变得不太清楚，这会使LOOCV结果的解释变得复杂。在本文中，我们提出了一个针对潜在高斯模型（包括具有结构性随机效应的人）定制的互补交叉验证框架。我们的方法与LOOCV不同，通过排除了从训练集中精心构造的集合，这更好地模拟了更长的预测条件。此外，我们通过调整这种修饰的交叉验证的完整关节后部来实现计算效率，从而消除了模型重新限制的需求。此方法是在R-Inla软件包（www.r-inla.org）中实现的，可以适应各种推论框架。
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations, LOOCV has since been extended to other cases such as hierarchical models. However, it focuses primarily on short-range prediction and may not fully capture long-range prediction scenarios. For structured hierarchical models, particularly those involving multiple random effects, the concepts of short- and long-range predictions become less clear, which can complicate the interpretation of LOOCV results. In this paper, we propose a complementary cross-validation framework specifcally tailored for longer-range prediction in latent Gaussian models, including those with structured random effects. Our approach differs from LOOCV by excluding a carefully constructed set from the training set, which better emulates longer-range prediction conditions. Furthermore, we achieve computational effciency by adjusting the full joint posterior for this modifed cross-validation, thus eliminating the need for model reftting. This method is implemented in the R-INLA package (www.r-inla.org) and can be adapted to a variety of inferential frameworks.
