Speaker: Guorong Dai, Fudan University

Time: 14:00-15:00 p.m., March 28, 2024, GMT+8

Venue: Room 225, Siyuan Hall, Zhihua Building, PKU 

Abstract: 

In a nonparametric regression setting, we propose a novel concept of ''individual variable importance'', which refers to the relevance of some covariates with respect to an outcome variable among individuals with certain features. This concept holds practical importance for both risk assessment and association identification. For example, it can represent (i) the usefulness of expensive biomarkers in disease prediction for individuals at certain baseline risk, or (ii) age-specific associations between physiological indicators. We quantify the individual variable importance by a ratio parameter between two conditional mean squared errors. To infer this parameter we develop fully nonparametric estimators and establish their asymptotic properties. Our inferential approaches perform well in simulation studies. We further demonstrate our approaches through application to a real data set, showing a scientifically interesting result: the association between body shape and systolic blood pressure decays with increasing age. While our finding aligns with the existing medical literature based on standard parametric regression techniques, our analysis methods are more reliable because their validity is not affected by model misspecification. More importantly, the fully nonparametric nature equips the individual variable importance framework with broader applicability in contexts that go beyond traditional parametric modeling. It can capture complex relationships between variables that are likely to be missed by standard parametric interaction analyses.

Source: School of Mathematical Sciences , PKU