Learning Dynamic Graphs under Partial Observability

This work examines the problem of learning a network graph from signals emitted by the network nodes, according to a diffusion model ruled by a Laplacian combination policy. The challenging regime of partial observability is considered, where signals are collected from a limited subset of nodes, and we wish to estimate the subgraph of connections between these probed nodes. For the static setting where the network graph is fixed during the estimation process, we examine the sample complexity (number of time samples necessary to achieve consistent learning as the network size grows) of Erdős-Rényi and Bollobás-Riordan graphs. This complexity is almost quadratic for the former and almost linear for the latter class of graphs. We then examine the dynamic graph setting where the graph of latent nodes grows over time, while the probed subset remains fixed. We show that in this case the sample complexity can be reduced, implying the unexpected conclusion that dynamic graphs might help topology inference under partial observability.