Title: Solving Continual Learning via Problem Decomposition. Abstract: This paper is concerned with class incremental learning (CIL) in continual learning (CL). CIL is the popular continual learning paradigm in which a system receives a sequence of tasks with different classes in each task and is expected to learn to predict the class of each test instance without given any task related information for the instance. Although many techniques have been proposed to solve CIL, it remains to be highly challenging due to the difficulty of dealing with catastrophic forgetting (CF). This paper starts from the first principle and proposes a novel method to solve the problem. The definition of CIL reveals that the problem can be decomposed into two probabilities: within-task prediction probability and task-id prediction probability. This paper proposes an effective technique to estimate these two probabilities based on the estimation of feature distributions in the latent space using incremental PCA and Mahalanobis distance. The proposed method does not require a memory buffer to save replay data and it outperforms strong baselines including replay-based methods.