Diffusion Model for Relational Inference in Interacting Systems

Dynamic behaviors of complex interacting systems, ubiquitously found in physical, biological, engineering, and social phenomena, are associated with underlying interactions between components of the system. A fundamental challenge in network science is to uncover interaction relationships between network components solely from observational data on their dynamics. Recently, generative models in machine learning, such as the variational autoencoder, have been used to identify the network structure through relational inference in multivariate time series data. However, most existing approaches are based on time series predictions, which are still challenging in the presence of missing data. In this study, we propose a novel approach, <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Diff</b>usion model for <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b>elational <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</b>nference (DiffRI), inspired by a self-supervised method for probabilistic time series imputation. DiffRI learns to infer the existence probability of interactions between network components through conditional diffusion modeling. Numerical experiments on both synthetic and quasi-real datasets show that DiffRI is highly competent with other well-known methods in discovering ground truth interactions. Furthermore, we demonstrate that our imputation-based approach is more tolerant of missing data than prediction-based approaches.