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Most recent approaches to monocular 3D pose estimation rely on Deep Learning. They either train a Convolutional Neural Network to directly regress from image to 3D pose, which ignores the dependencies between human joints, or model these dependencies via a max-margin structured learning framework, which involves a high computational cost at inference time. In this paper, we introduce a Deep Learning regression architecture for structured prediction of 3D human pose from monocular images that relies on an overcomplete autoencoder to learn a high-dimensional latent pose representation and account for joint dependencies. We demonstrate that our approach outperforms state-of-the-art ones both in terms of structure preservation and prediction accuracy.