A more efficient method for large-sample model-free feature screening via multi-armed bandits

2025-09-19

AI Summary

To address the computational bottleneck of model-agnostic feature screening for ultra-large-scale, ultra-high-dimensional data, this paper proposes CR-SIS—a rank-correlation-based screening method—and its efficient online variant, BanditCR-SIS. Innovatively integrating the multi-armed bandit framework into feature ranking, the approach combines Chatterjee’s rank correlation coefficient, randomized sampling, and dynamic priority scheduling. It guarantees theoretical convergence and stability while reducing time complexity from $O(n log n cdot p)$ to $O(sqrt{n} log n cdot p + n log n)$. Experiments on synthetic and real-world datasets demonstrate that the method achieves high screening accuracy with minimal computational overhead. Notably, it enables the first scalable, online feature screening for high-dimensional data, establishing a novel, extensible paradigm for detecting nonlinear relationships in massive datasets.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider the model-free feature screening in large-scale ultrahigh-dimensional data analysis. Existing feature screening methods often face substantial computational challenges when dealing with large sample sizes. To alleviate the computational burden, we propose a rank-based model-free sure independence screening method (CR-SIS) and its efficient variant, BanditCR-SIS. The CR-SIS method, based on Chatterjee's rank correlation, is as straightforward to implement as the sure independence screening (SIS) method based on Pearson correlation introduced by Fan and Lv(2008), but it is significantly more powerful in detecting nonlinear relationships between variables. Motivated by the multi-armed bandit (MAB) problem, we reformulate the feature screening procedure to significantly reduce the computational complexity of CR-SIS. For a predictor matrix of size n imes p, the computational cost of CR-SIS is O(nlog(n)p), while BanditCR-SIS reduces this to O(sqrt(n)log(n)p + nlog(n)). Theoretically, we establish the sure screening property for both CR-SIS and BanditCR-SIS under mild regularity conditions. Furthermore, we demonstrate the effectiveness of our methods through extensive experimental studies on both synthetic and real-world datasets. The results highlight their superior performance compared to classical screening methods, requiring significantly less computational time.

Problem

• Efficient model-free feature screening for ultrahigh-dimensional data
• Reducing computational complexity in large-sample nonlinear relationship detection
• Overcoming computational challenges of existing feature screening methods

Innovation

• Rank-based model-free screening via Chatterjee correlation
• Multi-armed bandit reformulation reduces computational complexity
• Achieves O(√n log(n)p + n log(n)) time complexity