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

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Bhutani, Mukul, Kolter, J Zico
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.03.2023
Subjects
Computer Science - Learning
Computer Science - Social and Information Networks
Dynamical systems
Mass flow
Predictions
Social networks
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2303.07675