Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model actually learns the underlying dynamics. We therefore propose a constrained optimisation framework as a general approach for training DSSMs. Building upon this, we introduce the extended Kalman VAE (EKVAE), which combines amortised variational inference with classic Bayesian filtering/smoothing to model dynamics more accurately than RNN-based DSSMs. Our results show that the constrained optimisation framework significantly improves system identification and prediction accuracy on the example of established state-of-the-art DSSMs. The EKVAE outperforms previous models w.r.t. prediction accuracy, achieves remarkable results in identifying dynamical systems, and can furthermore successfully learn state-space representations where static and dynamic features are disentangled.

Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact latent space. Prevalent is the use of the Euclidean metric, which has the drawback of ignoring information about similarity of data stored in the decoder, as captured by the framework of Riemannian geometry. We propose an extension to the framework of variational auto-encoders allows learning flat latent manifolds, where the Euclidean metric is a proxy for the similarity between data points. This is achieved by defining the latent space as a Riemannian manifold and by regularising the metric tensor to be a scaled identity matrix. Additionally, we replace the compact prior typically used in variational auto-encoders with a recently presented, more expressive hierarchical one—and formulate the learning problem as a constrained optimisation problem. We evaluate our method on a range of data-sets, including a video-tracking benchmark, where the performance of our unsupervised approach nears that of state-of-the-art supervised approaches, while retaining the computational efficiency of straight-line-based approaches.

We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we formulate the learning problem as a constrained optimisation problem by extending the Taming VAEs framework to two-level hierarchical models. We introduce a graph-based interpolation method, which shows that the topology of the learned latent representation corresponds to the topology of the data manifold---and present several examples, where desired properties of latent representation such as smoothness and simple explanatory factors are learned by the prior.

Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source—the latent space—to samples from a more complex distribution represented by a dataset. While the manifold hypothesis implies that a dataset contains large regions of low density, the training criterions of VAEs and GANs will make the latent space densely covered. Consequently points that are separated by low-density regions in observation space will be pushed together in latent space, making stationary distances poor proxies for similarity. We transfer ideas from Riemannian geometry to this setting, letting the distance between two points be the shortest path on a Riemannian manifold induced by the transformation. The method yields a principled distance measure, provides a tool for visual inspection of deep generative models, and an alternative to linear interpolation in latent space. In addition, it can be applied for robot movement generalization using previously learned skills. The method is evaluated on a synthetic dataset with known ground truth; on a simulated robot arm dataset; on human motion capture data; and on a generative model of handwritten digits.

Robots can rapidly acquire new skills from demonstrations. However, during generalisation of skills or transitioning across fundamentally different skills, it is unclear whether the robot has the necessary knowledge to perform the task. Failing to detect missing information often leads to abrupt movements or to collisions with the environment. Active learning can quantify the uncertainty of performing the task and, in general, locate regions of missing information. We introduce a novel algorithm for active learning and demonstrate its utility for generating smooth trajectories. Our approach is based on deep generative models and metric learning in latent spaces. It relies on the Jacobian of the likelihood to detect non-smooth transitions in the latent space, i.e., transitions that lead to abrupt changes in the movement of the robot. When non-smooth transitions are detected, our algorithm asks for an additional demonstration from that specific region. The newly acquired knowledge modifies the data manifold and allows for learning a latent representation for generating smooth movements. We demonstrate the efficacy of our approach on generalising elementary skills, transitioning across different skills, and implicitly avoiding collisions with the environment. For our experiments, we use a simulated pendulum where we observe its motion from images and a 7-DoF anthropomorphic arm.