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We consider the problem of learning robust models of robot motion through demonstration. An approach based on Hidden Markov Model (HMM) and Gaussian Mixture Regression (GMR) is proposed to extract redundancies across multiple demonstrations, and build a time-independent model of a set of movements demonstrated by a human user. Two experiments are presented to validate the method, that consist of learning to hit a ball with a robotic arm, and of teaching a humanoid robot to manipulate a spoon to feed another humanoid. The experiments demonstrate that the proposed model can efficiently handle several aspects of learning by imitation. We first show that it can be utilized in an unsupervised learning manner, where the robot is autonomously organizing and encoding variants of motion from the multiple demonstrations. We then show that the approach allows to robustly generalize the observed skill by taking into account multiple constraints in task space during reproduction.