Dear all,

You are all invited to this week's NOMADS seminar at GSSI. The seminar will be on Wednesday February 17 at 17:00 (CET) by Michael Schaub from RWTH Aachen University (Germany). The talk will be focused on a method for learning the structure of a network given few observations of a diffusive process on the unknown graph. Title and abstract are below.

To attend the semimar please use the following link: https://us02web.zoom.us/j/87171939595

Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/

Hope to see you all on Wednesday! And, please feel free to distribute this announcement as you see fit.

Francesco and Nicola

-------- Title: Learning from signals on graphs with unobserved edges

In many applications we are confronted with the following system identification scenario: we observe a dynamical process that describes the state of a system at particular times. Based on these observations we want to infer the (dynamical) interactions between the entities we observe. 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 we can obtain from such a process are far too few to identify the edges of the network exactly. Can we still reliably infer some aspects of the underlying system?

Motivated by this question we consider the following identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes.  More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic blockmodel (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy. We further discuss some possible variations and extensions of this problem setup.

— Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io