Nonparametric Testing Under Randomized Sketching.

Area of Science:

• Statistics
• Machine Learning
• Computational Complexity

Background:

• Nonparametric inference faces computational challenges with large datasets.
• Efficient statistical testing is crucial for data analysis and model performance.
• Kernel ridge regression is a powerful tool in machine learning.

Purpose of the Study:

• To develop computationally efficient nonparametric testing methods.
• To address the high computational complexity of nonparametric inference for large data.
• To establish theoretical guarantees for the proposed testing strategy.

Main Methods:

• Employing a random projection strategy for computational efficiency.
• Proposing a simple distance-based test statistic within the kernel ridge regression framework.
• Deriving the minimum number of random projections for testing optimality (minimax rate).
• Establishing an adaptive testing procedure without prior knowledge of regularity.

Main Results:

• Demonstrated computational efficiency in nonparametric testing.
• Achieved testing optimality in terms of the minimax rate.
• Developed an adaptive procedure applicable without prior regularity assumptions.
• Established theoretical upper bounds for empirical kernel eigenvalues.

Conclusions:

• Random projection strategy significantly enhances computational efficiency for nonparametric testing.
• The proposed methods offer a robust and adaptive approach to statistical inference.
• Theoretical findings are supported by simulations and real-world data analysis.