Title: Mixup Training as the Complexity Reduction. Abstract: Machine learning models often suffer from the problem of over-fitting. Many data augmentation methods have been proposed to tackle such a problem, and one of them is called mixup. Mixup is a recently proposed regularization procedure, which linearly interpolates a random pair of training examples. This regularization method works very well experimentally, but its theoretical guarantee is not adequately discussed. In this study, we aim to discover why mixup works well from the aspect of the statistical learning theory. In addition, we reveal how the effect of mixup changes in each situation. Furthermore, we also investigated the effects of changes in the parameter of mixup. Our work contributes to searching for the optimal parameters and estimating the effects of the parameters currently used. The results of this study provide a theoretical clarification of when and how effective regularization by mixup is.