This paper investigates a range of empirical risk functions and regularization methods suitable for self-training methods in semi-supervised learning. These approaches draw inspiration from various divergence measures, such as $f$-divergences and $\alpha$-R\'enyi divergences. Inspired by the theoretical foundations rooted in divergences, i.e., $f$-divergences and $\alpha$-R\'enyi divergence, we also provide valuable insights to enhance the understanding of our empirical risk functions and regularization techniques. In the pseudo-labeling and entropy minimization techniques as self-training methods for effective semi-supervised learning, the self-training process has some inherent mismatch between the true label and pseudo-label (noisy pseudo-labels) and some of our empirical risk functions are robust, concerning noisy pseudo-labels. Under some conditions, our empirical risk functions demonstrate better performance when compared to traditional self-training methods.

研究了适用于半监督学习中自训练方法的一系列经验风险函数和正则化方法，这些方法受到各种差异度量的启示。通过对差异度量理论基础的启发，即差异度量和Rényi差异度量，我们还提供了有益的见解，以增强对我们的经验风险函数和正则化技术的理解。在伪标签和熵最小化技术中，作为有效半监督学习的自训练方法，自训练过程存在真实标签和伪标签之间的不匹配（噪声伪标签），我们的一些经验风险函数在处理噪声伪标签方面表现出稳健性。在一些条件下，与传统的自训练方法相比，我们的经验风险函数表现出更好的性能。

基于$f$-散度和$α$-Rényi散度的鲁棒半监督学习