Sinkhorn-Flow: Predicting Probability Mass Flow in Dynamical Systems Using Optimal Transport
This addresses the need for understanding mass flow in time series forecasting, particularly for social network community evolution, though it appears incremental as it builds on existing optimal transport and deep learning techniques.
The paper tackles the problem of predicting how probability mass flows between discrete variables over time in dynamical systems, introducing Sinkhorn-Flow which uses optimal transport to predict transport matrices in deep learning systems, and shows substantial improvements over alternative methods on tasks like predicting faction evolution in Ukrainian parliamentary voting.
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.