Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Bounds

Abstract: The PAC-Bayesian framework has significantly advanced the understanding of statistical learning, particularly for majority voting methods. Despite its successes, its application to multi-view learning -- a setting with multiple complementary data representations -- remains underexplored. In this work, we extend PAC-Bayesian theory to multi-view learning, introducing novel generalization bounds based on R\'enyi divergence. These bounds provide an alternative to traditional Kullback-Leibler divergence-based counterparts, leveraging the flexibility of R\'enyi divergence. Furthermore, we propose first- and second-order oracle PAC-Bayesian bounds and extend the C-bound to multi-view settings. To bridge theory and practice, we design efficient self-bounding optimization algorithms that align with our theoretical results.