Oracle inequalities for network models and sparse graphon estimation

Understand

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models.

• We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network.
• Taking the stochastic block model as an approximation, we construct estimators of network connection probabilities -- the ordinary block constant least squares estimator, and its restricted version.
• We show that they satisfy oracle inequalities with respect to the block constant oracle.