# Blind identification of stochastic block models from dynamical observations

## TL;DR

This paper introduces spectral algorithms for blind identification of stochastic block models from dynamical observations, enabling recovery of network structure and parameters without direct edge knowledge.

## Contribution

It presents novel spectral methods with provable guarantees for inferring SBM partitions and parameters solely from nodal diffusive process observations.

## Key findings

- Spectral algorithms achieve high-accuracy partition recovery.
- The methods are supported by theoretical guarantees based on random matrix theory.
- Numerical experiments validate the effectiveness of the proposed algorithms.

## Abstract

We consider a blind identification problem in which we aim to recover a statistical model of a network without knowledge of the network's edges, but based solely on nodal observations of a certain process. More concretely, we focus on observations that consist of single snapshots taken from multiple trajectories of a diffusive process that evolves over the unknown network. We model the network as generated from an independent draw from a latent stochastic block model (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We discuss some non-identifiability issues related to this problem and present simple spectral algorithms that provably solve the partition recovery and parameter estimation problems with high accuracy. Our analysis relies on recent results in random matrix theory and covariance estimation, and associated concentration inequalities. We illustrate our results with several numerical experiments.