Olga Klopp. Network models and sparse graphon estimation.

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 and derive optimal rates of convergence for this problem. Our results cover the important setting of sparse networks. We also establish upper bounds on the minimax risk for graphon estimation when the probability matrix is sampled according to a graphon model.