Unsupervised relational inference using masked reconstruction

Abstract

Problem setting: Stochastic dynamical systems in which local interactions give rise to complex emerging phenomena are ubiquitous in nature and society. This work explores the problem of inferring the unknown interaction structure (represented as a graph) of such a system from measurements of its constituent agents or individual components (represented as nodes). We consider a setting where the underlying dynamical model is unknown and where different measurements (i.e., snapshots) may be independent (e.g., may stem from different experiments). Method: Our method is based on the observation that the temporal stochastic evolution manifests itself in local patterns. We show that we can exploit these patterns to infer the underlying graph by formulating a masked reconstruction task. Therefore, we propose GINA (Graph Inference Network Architecture), a machine learning approach to simultaneously learn the latent interaction graph and, conditioned on the interaction graph, the prediction of the (masked) state of a node based only on adjacent vertices. Our method is based on the hypothesis that the ground truth interaction graph—among all other potential graphs—allows us to predict the state of a node, given the states of its neighbors, with the highest accuracy. Results: We test this hypothesis and demonstrate GINA’s effectiveness on a wide range of interaction graphs and dynamical processes. We find that our paradigm allows to reconstruct the ground truth interaction graph in many cases and that GINA outperforms statistical and machine learning baseline on independent snapshots as well as on time series data.