SOM-VAE: Interpretable Discrete Representation Learning on Time Series

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most 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 a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation 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 in terms of clustering performance and interpretability 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 on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on Learning Representations (ICLR 2019

Probabilistic Models for Exploring, Predicting, and Influencing Health Trajectories

Over the past decade, healthcare systems around the world have transitioned from paper to electronic health records. The majority of healthcare systems today now host large, on-premise clusters that support an institution-wide network of computers deployed at the point of care. A stream of transactions pass through this network each minute, recording information about what medications a patient is receiving, what procedures they have had, and the results of hundreds of physical examinations and laboratory tests. There is increasing pressure to leverage these repositories of data as a means to improve patient outcomes, drive down costs, or both. To date, however, there is no clear answer on how to best do this. In this thesis, we study two important problems that can help to accomplish these goals: disease subtyping and disease trajectory prediction. In disease subtyping, the goal is to better understand complex, heterogeneous diseases by discovering patient populations with similar symptoms and disease expression. As we discover and refine subtypes, we can integrate them into clinical practice to improve management and can use them to motivate new hypothesis-driven research into the genetic and molecular underpinnings of the disease. In disease trajectory prediction, our goal is to forecast how severe a patient's disease will become in the future. Tools to make accurate forecasts have clear implications for clinical decision support, but they can also improve our process for validating new therapies through trial enrichment. We identify several characteristics of EHR data that make it to difficult to do subtyping and disease trajectory prediction. The key contribution of this thesis is a collection of novel probabilistic models that address these challenges and make it possible to successfully solve the subtyping and disease trajectory prediction problems using EHR data