This paper presents a theory of learning from different domains, focusing on domain adaptation and transfer learning. The authors investigate two key questions: under what conditions can a classifier trained on source data perform well on a target domain with a different distribution, and how to combine labeled source and target data to minimize target error. They introduce the HΔH-divergence, a measure of divergence between domains that can be estimated from unlabeled data. This divergence is used to bound the target error of a classifier trained on source data. The authors also show how to choose the optimal combination of source and target error based on domain divergence, sample sizes, and hypothesis complexity. Their results generalize previous work and provide tighter bounds than those that consider only source or target error. The paper also discusses the application of these results to sentiment classification, showing that non-trivial settings of the combination parameter α perform better than baseline settings. The authors conclude with a discussion of future research directions in domain adaptation.This paper presents a theory of learning from different domains, focusing on domain adaptation and transfer learning. The authors investigate two key questions: under what conditions can a classifier trained on source data perform well on a target domain with a different distribution, and how to combine labeled source and target data to minimize target error. They introduce the HΔH-divergence, a measure of divergence between domains that can be estimated from unlabeled data. This divergence is used to bound the target error of a classifier trained on source data. The authors also show how to choose the optimal combination of source and target error based on domain divergence, sample sizes, and hypothesis complexity. Their results generalize previous work and provide tighter bounds than those that consider only source or target error. The paper also discusses the application of these results to sentiment classification, showing that non-trivial settings of the combination parameter α perform better than baseline settings. The authors conclude with a discussion of future research directions in domain adaptation.