Towards the Generalization of Multi-view Learning: An Information-theoretical Analysis

2025-01-28

AI Summary

Multi-view learning lacks theoretical foundations for generalization, particularly in predicting model performance on unseen scenarios involving reconstruction and classification. Method: We establish the first information-theoretic unified generalization error bound, explicitly characterizing how consensus and complementary information influence representation disentanglement and generalization. We propose an information-bottleneck-regularized framework with provable generalization guarantees, designing data-dependent leave-one-out and supersample bounds, and deriving fast-rate convergence bounds in the interpolation regime. Contribution/Results: Our theoretical analysis yields a tight, computationally tractable upper bound on generalization error, revealing the synergistic interplay between consensus and complementary information. Empirical evaluation demonstrates strong correlation between the derived bound and actual generalization gaps, significantly enhancing interpretability and predictive capability for multi-view models.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Representation Learning for Vision
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Multiview learning has drawn widespread attention for its efficacy in leveraging cross-view consensus and complementarity information to achieve a comprehensive representation of data. While multi-view learning has undergone vigorous development and achieved remarkable success, the theoretical understanding of its generalization behavior remains elusive. This paper aims to bridge this gap by developing information-theoretic generalization bounds for multi-view learning, with a particular focus on multi-view reconstruction and classification tasks. Our bounds underscore the importance of capturing both consensus and complementary information from multiple different views to achieve maximally disentangled representations. These results also indicate that applying the multi-view information bottleneck regularizer is beneficial for satisfactory generalization performance. Additionally, we derive novel data-dependent bounds under both leave-one-out and supersample settings, yielding computational tractable and tighter bounds. In the interpolating regime, we further establish the fast-rate bound for multi-view learning, exhibiting a faster convergence rate compared to conventional square-root bounds. Numerical results indicate a strong correlation between the true generalization gap and the derived bounds across various learning scenarios.

Problem

• Multi-view Learning
• Generalization Ability
• Image Reconstruction and Classification

Innovation

• Multi-view Learning
• Information Bottleneck
• Generalization Enhancement