Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Ultra-high dimensional data presents challenges in variable selection due to a large number of predictors.
• Traditional methods struggle with high dimensionality, leading to potential loss of important variables or inclusion of irrelevant ones.

Purpose of the Study:

• To develop a computationally efficient and model-agnostic framework for sufficient variable screening.
• To accurately identify relevant predictors in ultra-high dimensional settings while controlling for false discoveries.

Main Methods:

• A quantile-adaptive sufficient variable screening framework is proposed.
• A compound testing procedure using conditionally imputing marginal rank correlation at various response quantile levels is introduced.
• The method controls false discovery adaptively or via a prespecified threshold.

Main Results:

• The proposed testing statistic effectively captures sufficient dependence between predictors and the response variable.
• Theoretical properties are established under mild conditions, demonstrating robustness.
• Numerical studies, including simulations and real-world data analysis, show the framework performs well in practice.

Conclusions:

• The quantile-adaptive framework offers an efficient and reliable approach for variable screening in ultra-high dimensional data.
• The method's computational efficiency and ease of implementation make it suitable for practical applications.
• This framework aids in reducing dimensionality and improving the interpretability of complex datasets.