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We present a programming-by-demonstration framework for generically extracting the relevant features of a given task and for addressing the problem of generalizing the acquired knowledge to different contexts. We validate the architecture through a series of experiments, in which a human demonstrator teaches a humanoid robot simple manipulatory tasks. A probability-based estimation of the relevance is suggested by first projecting the motion data onto a generic latent space using principal component analysis. The resulting signals are encoded using a mixture of Gaussian/Bernoulli distributions (Gaussian mixture model/Bernoulli mixture model). This provides a measure of the spatio-temporal correlations across the different modalities collected from the robot, which can be used to determine a metric of the imitation performance. The trajectories are then generalized using Gaussian mixture regression. Finally, we analytically compute the trajectory which optimizes the imitation metric and use this to generalize the skill to different contexts