Diagnostic pathology and histopathology images play a critical role in the diagnosis and treatment of carcinomas. In order to achieve satisfactory performance, we usually need a large amount of labeled data. Annotating a large number of histopathology images for training machine learning models can be expensive and time-consuming. We explored several machine learning approaches in a low-data regime for histopathology images, leading to a caption generation model for histopathology images, a hyperbolic attention model for histopathology images, a deep Bayesian active learning method to enable efficient selection of training examples that can undergo expensive annotation, and representation learning approach that utilize existing coarse-grained labels of whole slide images to improve model performance on limited fine-grained data. Our experiments demonstrate that these approaches can improve the performances of models in the low-data regime while maintaining high levels of interpretability, minimizing labeling costs, and showing analytical advantages. The results of this study provide valuable insights for future research in the area of machine learning in low-data regimes for histopathology images.