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Predicting how distributions over discrete variables vary over time is acommon task in time series forecasting. But whereas most approaches focus onmerely predicting the distribution at subsequent time steps, a crucial piece ofinformation in many settings is to determine how this probability mass flowsbetween the different elements over time. We propose a new approach topredicting such mass flow over time using optimal transport. Specifically, wepropose a generic approach to predicting transport matrices in end-to-end deeplearning systems, replacing the standard softmax operation with Sinkhorniterations. We apply our approach to the task of predicting how communitieswill evolve over time in social network settings, and show that the approachimproves substantially over alternative prediction methods. We specificallyhighlight results on the task of predicting faction evolution in Ukrainianparliamentary voting.

Sinkhorn-Flow: Predicting Probability Mass Flow in Dynamical Systems Using Optimal Transport