Bayesian Predictive Synthesis for Dynamic Networks: Forecasting and Identifying Structural Mechanisms
For researchers analyzing dynamic networks, this work addresses the challenge of adapting to shifting structural mechanisms, offering both accurate forecasts and interpretable inference on which mechanism drives the network at each time step.
The paper develops a dynamic Bayesian predictive synthesis method for networks that combines multiple structural mechanisms (e.g., communities, geometry, hubs) with time-varying weights, enabling adaptive forecasting and identification of the dominant mechanism. The method provides calibrated edge forecasts and mechanism weights, with theoretical guarantees including a sharp threshold for distinguishability and optimal tracking of mechanism switches.
Networks are shaped by competing structural mechanisms, such as communities, geometry, or hubs. In a dynamic network the most predictive mechanism can change, and a model tied to one mechanism, or to fixed weights, cannot adapt as the dominant structure shifts. We develop dynamic Bayesian predictive synthesis for networks, in which a mechanism is an agent forecasting the next snapshot's edges and a synthesis layer combines them with time-varying weights. At each step the method returns a calibrated edge forecast and inference on the mechanism weights, with intervals valid given the fitted agents, so it also reports which mechanism is most informative. Inference of this kind requires a sparse-safe parametrization and an identification theory, under which a single graph identifies and estimates the weights. A sharp threshold separates distinguishable from indistinguishable mechanisms, a change in the active mechanism is tracked at an optimal per-switch cost, and for a single snapshot the method reduces to calibrated link prediction. On real networks, simulations, and benchmarks, the synthesis gives accurate, calibrated forecasts and recovers the leading mechanism when