论文标题
部分可观测时空混沌系统的无模型预测
Variable Importance Based Interaction Modeling with an Application on Initial Spread of COVID-19 in China
论文作者
论文摘要
线性回归模型与连续和分类预测因子的相互作用选择在现代科学的许多领域都有用，但是当预测因子的数量相对较大时，非常具有挑战性。现有的交互选择方法着重于寻找一个最佳模型。尽管有吸引力的属性（例如一致性和Oracle属性）已经为这种方法建立了很好的建立，但实际上它们在高维数据的稳定性方面可能会差，并且通常不会处理分类预测指标。在本文中，我们介绍了一个基于重要性的相互作用模型（VIBIM）程序，以在具有连续和分类预测指标的线性回归模型中学习相互作用。它提供了具有高稳定性和可解释性的多个强大候选模型。仿真研究表明了其良好的有限样本性能。我们将Vibim程序应用于Tian等人使用的2019年电晕病毒疾病（COVID-19）。 （2020）并衡量相关因素的影响，包括传输控制措施对COVID-19的扩散。我们表明，在可解释性，稳定性，可靠性和预测方面，Vibim方法会导致更好的模型。
Interaction selection for linear regression models with both continuous and categorical predictors is useful in many fields of modern science, yet very challenging when the number of predictors is relatively large. Existing interaction selection methods focus on finding one optimal model. While attractive properties such as consistency and oracle property have been well established for such methods, they actually may perform poorly in terms of stability for high-dimensional data, and they do not typically deal with categorical predictors. In this paper, we introduce a variable importance based interaction modeling (VIBIM) procedure for learning interactions in a linear regression model with both continuous and categorical predictors. It delivers multiple strong candidate models with high stability and interpretability. Simulation studies demonstrate its good finite sample performance. We apply the VIBIM procedure to a Corona Virus Disease 2019 (COVID-19) data used in Tian et al. (2020) and measure the effects of relevant factors, including transmission control measures on the spread of COVID-19. We show that the VIBIM approach leads to better models in terms of interpretability, stability, reliability and prediction.
