Title: ESTIMATING STOCHASTIC BLOCK MODELS IN THE PRESENCE OF COVARIATES (joint with Louise Laage)

Abstract: In the standard stochastic block model for networks, the probability of a connection between
two nodes, often referred to as the edge probability, depends on the unobserved communities
each of these nodes belongs to. We consider a flexible framework in which each edge probability, together
with the probability of community assignment, are also impacted by observed covariates. We
propose a computationally tractable two-step procedure to estimate the conditional edge probabilities
as well as the community assignment probabilities. The first step relies on a spectral clustering algorithm
applied to a localized adjacency matrix of the network. In the second step, k-nearest neighbor
regression estimates are computed on the extracted communities. We study the statistical properties
of these estimators by providing non-asymptotic bounds.