Title: Learning Causal Semantic Representation for Out-of-Distribution Prediction. Abstract: Conventional supervised learning methods, especially deep ones, are found to be sensitive to out-of-distribution (OOD) examples, largely because the learned representation mixes the semantic factor with the variation factor due to their domain-specific correlation, while only the semantic factor causes the output. To address the problem, we propose a Causal Semantic Generative model (CSG) based on causality to model the two factors separately, and learn it on a single training domain for prediction without (OOD generalization) or with unsupervised data (domain adaptation) in a test domain. We prove that CSG identifies the semantic factor on the training domain, and the invariance principle of causality subsequently guarantees the boundedness of OOD generalization error and the success of adaptation. We also design novel and delicate learning methods for both effective learning and easy prediction, following the first principle of variational Bayes and the graphical structure of CSG. Empirical study demonstrates the effect of our methods to improve test accuracy for OOD generalization and domain adaptation.