Local Rademacher Complexity: sharper risk bounds with and without unlabeled samples

Area of Science:

• Machine Learning
• Statistical Learning Theory

Background:

• Generalization bounds are crucial for understanding model performance.
• Existing bounds often require fully labeled datasets, limiting their applicability.
• Leveraging unlabeled data can potentially improve generalization without additional labeling costs.

Purpose of the Study:

• To introduce a novel Local Rademacher Complexity risk bound.
• To demonstrate the utility of unlabeled samples in enhancing generalization bounds.
• To improve upon the state-of-the-art in generalization error estimation.

Main Methods:

• Derivation of a new Local Rademacher Complexity measure.
• Theoretical analysis of the proposed risk bound.
• Comparison with existing generalization bounds in machine learning.

Main Results:

• A new risk bound is established using Local Rademacher Complexity.
• The bound effectively incorporates unlabeled data for improved generalization assessment.
• The proposed bound outperforms existing methods, even when no unlabeled data is used.

Conclusions:

• The new Local Rademacher Complexity bound offers a powerful tool for generalization analysis.
• Unlabeled data can significantly enhance the performance of generalization bounds.
• This work advances the theoretical understanding of model generalization in machine learning.