Time series are often associated with missing values, for instance due to faulty measurement devices, partially observed states, or costly measurement procedures [15]. These missing values impair the usefulness and interpretability of the data, leading to the problem of data imputation: estimating those missing values from the observed ones [38]. Multivariate time series, consisting of multiple correlated univariate time series or channels, give rise to two distinct ways of imputing missing information: (1) by exploiting temporal correlations within each channel, and (2) by exploiting correlations across channels, for example by using lowerdimensional representations of the data. For instance in a medical setting, if the blood pressure of a patient is unobserved, it can be informative that the heart rate at the current time is higher than normal and that the blood pressure was also elevated an hour ago. An ideal imputation model for multivariate time series should therefore take both of these sources of information into account.

Fitting machine learning models in the low-data limit is challenging. The main challenge is to obtain suitable prior knowledge and encode it into the model, for instance in the form of a Gaussian process prior. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge from data acquired in related tasks. When it comes to meta-learning in Gaussian process models, approaches in this setting have mostly focused on learning the kernel function of the prior, but not on learning its mean function. In this work, we propose to parameterize the mean function of a Gaussian process with a deep neural network and train it with a meta-learning procedure. We present analytical and empirical evidence that mean function learning can be superior to kernel learning alone, particularly if data is scarce.

Kernel methods on discrete domains have shown great promise for many challenging tasks, e.g., on biological sequence data as well as on molecular structures. Scalable kernel methods like support vector machines offer good predictive performances but they often do not provide uncertainty estimates. In contrast, probabilistic kernel methods like Gaussian Processes offer uncertainty estimates in addition to good predictive performance but fall short in terms of scalability. We present the first sparse Gaussian Process approximation framework on discrete input domains. Our framework achieves good predictive performance as well as uncertainty estimates using different discrete optimization techniques. We present competitive results comparing our framework to support vector machine and full Gaussian Process baselines on synthetic data as well as on challenging real-world DNA sequence data.

Human professionals are often required to make decisions based on complex multivariate time series measurements in an online setting, e.g. in health care. Since human cognition is not optimized to work well in high-dimensional spaces, these decisions benefit from interpretable low-dimensional representations. However, many representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose to couple a variational autoencoder to a discrete latent space and introduce a topological structure through the use of self-organizing maps. This allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the latent space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application. In the latter experiment, our representation uncovers meaningful structure in the acute physiological state of a patient.

We present a novel approach to modeling stories using recurrent neural networks. Different story features are extracted using natural language processing techniques and used to encode the stories as sequences. These sequences can be learned by deep neural networks, in order to predict the next story events. The predictions can be used as an inspiration for writers who experience a writer's block. We further assist writers in their creative process by generating visualizations of the character interactions in the story. We show that suggestions from our model are rated as highly as the real scenes from a set of films and that our visualizations can help people in gaining deeper story understanding.