B0464
Title: Learning from networks with unobserved edges
Authors: Michael Schaub - RWTH Aachen University (Germany) [presenting]
Abstract: In many applications, the following system identification scenario is confronted with: a dynamical process is observed that describes the state of a system at particular times. Based on these observations, dynamical interactions are inferred between the entities observed. In the context of a distributed system, this typically corresponds to a "network identification" task: find the weighted edges of the graph of interconnections. However, often, the number of samples obtained from such a process is far too few to identify the edges of the network exactly. Can one still reliably infer some aspects of the underlying system? Motivated by this question, the following identification problem is considered: instead of trying to infer the exact network, the aim is to recover a low-dimensional statistical model of the network based on the observed signals on the nodes. More concretely, the focus is on observations that consist of snapshots of a diffusive process that evolves over the unknown network. The model of the unobserved network is generated from an independent draw from a latent stochastic block model (SBM), and the goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. Simple spectral algorithms are presented that provably solve the partition and parameter inference problems with high accuracy. Some possible variations and extensions of this problem setup are further discussed.
