Abstract:The PAC-Bayesian framework has significantly advanced our understanding of statistical learning, particularly in majority voting methods. However, its application to multi-view learning remains underexplored. In this paper, we extend PAC-Bayesian theory to the multi-view setting, introducing novel PAC-Bayesian bounds based on R\'enyi divergence. These bounds improve upon traditional Kullback-Leibler divergence and offer more refined complexity measures. We further propose first and second-order oracle PAC-Bayesian bounds, along with an extension of the C-bound for multi-view learning. To ensure practical applicability, we develop efficient optimization algorithms with self-bounding properties.
Abstract:This paper presents a series of new results for domain adaptation in the multi-view learning setting. The incorporation of multiple views in the domain adaptation was paid little attention in the previous studies. In this way, we propose an analysis of generalization bounds with Pac-Bayesian theory to consolidate the two paradigms, which are currently treated separately. Firstly, building on previous work by Germain et al., we adapt the distance between distribution proposed by Germain et al. for domain adaptation with the concept of multi-view learning. Thus, we introduce a novel distance that is tailored for the multi-view domain adaptation setting. Then, we give Pac-Bayesian bounds for estimating the introduced divergence. Finally, we compare the different new bounds with the previous studies.