  Predicting how distributions over discrete variables vary over time is a
common task in time series forecasting. But whereas most approaches focus on
merely predicting the distribution at subsequent time steps, a crucial piece of
information in many settings is to determine how this probability mass flows
between the different elements over time. We propose a new approach to
predicting such mass flow over time using optimal transport. Specifically, we
propose a generic approach to predicting transport matrices in end-to-end deep
learning systems, replacing the standard softmax operation with Sinkhorn
iterations. We apply our approach to the task of predicting how communities
will evolve over time in social network settings, and show that the approach
improves substantially over alternative prediction methods. We specifically
highlight results on the task of predicting faction evolution in Ukrainian
parliamentary voting.
