We develop generalization bounds for transductive learning algorithms in the context of information theory and PAC-Bayesian theory, covering both the random sampling setting and the random splitting setting. We show that the transductive generalization gap can be bounded by the mutual information between training labels selection and the hypothesis. By introducing the concept of transductive supersamples, we translate results depicted by various information measures from the inductive learning setting to the transductive learning setting. We further establish PAC-Bayesian bounds with weaker assumptions on the loss function and numbers of training and test data points. Finally, we present the upper bounds for adaptive optimization algorithms and demonstrate the applications of results on semi-supervised learning and graph learning scenarios. Our theoretic results are validated on both synthetic and real-world datasets.

翻译：我们在信息论与PAC-Bayesian理论框架下，针对随机抽样设置和随机划分设置，建立了转导学习算法的泛化界。研究表明，转导泛化间隙可由训练标签选择与假设之间的互信息界定。通过引入转导超样本概念，我们将多种信息度量描述的结论从归纳学习场景迁移至转导学习场景。进一步地，我们在损失函数及训练/测试数据点数量约束更弱的条件下建立了PAC-Bayesian界。最后，我们提出了自适应优化算法的上界，并展示了相关结论在半监督学习和图学习场景中的应用。理论结果在合成数据集与真实数据集上均得到验证。