论文标题

在变量选择中使用参考模型

Using reference models in variable selection

论文作者

Pavone, Federico, Piironen, Juho, Bürkner, Paul-Christian, Vehtari, Aki

论文摘要

可变选择,或更一般的减少模型是统计工作流的重要方面,目的是提供数据的见解。在本文中,我们讨论并演示了在变量选择中使用参考模型的好处。参考模型通过建模其数据生成机制来充当目标变量上的噪声过滤器。结果,在模型选择过程中使用参考模型预测会降低可变性并提高稳定性,从而改善模型选择性能。假设贝叶斯参考模型很好地描述了未来数据的真实分布,那么参考模型的理论优先使用是将其预测分布投影到简化的模型,从而导致投影预测性变量选择方法。或者,参考模型也可以与常见的变量选择方法结合使用。在几个数值实验中,我们研究了带有或不带有参考模型的替代变量选择方法的投影预测方法的性能。我们的结果表明,参考模型的使用通常转化为更好,更稳定的变量选择。此外,我们证明,与替代变量选择方法相比,投影预测方法表现出卓越的性能,而不是使用参考模型。

Variable selection, or more generally, model reduction is an important aspect of the statistical workflow aiming to provide insights from data. In this paper, we discuss and demonstrate the benefits of using a reference model in variable selection. A reference model acts as a noise-filter on the target variable by modeling its data generating mechanism. As a result, using the reference model predictions in the model selection procedure reduces the variability and improves stability leading to improved model selection performance. Assuming that a Bayesian reference model describes the true distribution of future data well, the theoretically preferred usage of the reference model is to project its predictive distribution to a reduced model leading to projection predictive variable selection approach. Alternatively, reference models may also be used in an ad-hoc manner in combination with common variable selection methods. In several numerical experiments, we investigate the performance of the projective prediction approach as well as alternative variable selection methods with and without reference models. Our results indicate that the use of reference models generally translates into better and more stable variable selection. Additionally, we demonstrate that the projection predictive approach shows superior performance as compared to alternative variable selection methods independently of whether or not they use reference models.

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