Abstract: Aiming at the movement representation and generalization problems in imitation learning, a cross entropy optimization algorithm is proposed to infer parameters in mixture models. The proposed algorithm is easy to implement and computationally efficient. More importantly, it can automatically determine the optimal component number in the mixture models. In order to produce generalized motion trajectories, a cross entropy regression algorithm is proposed. To further improve the adaptability of the algorithm in dynamic environments, the concept of task parametrization is introduced and a task-parameterized cross entropy regression algorithm is proposed. Finally, a novel hammer-over-a-nail task is designed, which verifies the theoretical correctness and superiority of the proposed methods. Simulation experiments based on robot physical simulation software Gazebo show the feasibility of the proposed algorithms in piratical applications.