Abstract

The rapid accumulation of data across scientific disciplines has intensified the challenges of high-dimensional analysis, particularly in settings where the number of predictors exceeds the sample size. Conventional model-based screening procedures rely on strong distributional assumptions and often fail to detect nonlinear or interactive relationships among predictors. Model-free approaches, such as Conditional Characteristic Feature Screening (CCFS), improve screening performance in terms of robustness and computational efficiency; however, they are primarily limited to capturing marginal dependence structures. To address this limitation, this paper proposes an extended framework—Conditional Characteristic Feature Screening with Interaction (CCFI)—which explicitly incorporates interaction effects into the screening process. The proposed method employs conditional characteristic functions to capture both marginal and joint dependencies without imposing parametric modeling assumptions, thereby enabling the identification of higher-order relationships in ultra-high-dimensional settings. Theoretical analysis establishes the sure screening property and ranking consistency of the CCFI procedure under mild regularity conditions.