Generalization Analysis of Pairwise Learning for Ranking With Deep Neural Networks

Area of Science:

• Machine Learning
• Deep Learning
• Ranking Algorithms

Background:

• Pairwise learning is crucial for tasks like ranking, similarity learning, and AUC maximization.
• Existing theoretical understanding of deep neural networks in pairwise learning, especially for ranking, is limited.

Purpose of the Study:

• To apply symmetric deep neural networks to pairwise learning for ranking.
• To provide a theoretical generalization analysis for this algorithm.
• To address the lack of theoretical understanding in deep pairwise learning for ranking.

Main Methods:

• Utilized symmetric deep neural networks with a hinge loss (ϕh) for pairwise ranking.
• Performed generalization analysis by characterizing the risk-minimizing function.
• Employed tools from U-statistics and approximation theory for analysis.

Main Results:

• Designed two-part deep neural networks with shared weights, inducing an antisymmetric property.
• Presented convergence rates for approximation error based on function smoothness and noise conditions.
• Derived an excess generalization error bound using properties of the deep neural network hypothesis space.

Conclusions:

• The study provides a theoretical foundation for using symmetric deep neural networks in pairwise learning for ranking.
• The developed algorithm demonstrates theoretical guarantees on approximation and generalization errors.
• This work contributes to a better understanding of deep learning models in pairwise learning tasks.