Maximum likelihood estimation of sparse networks with missing observations

Abstract

Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the inhomogeneous random graph model with missing observations. Using the Stochastic Block Model as a parametric proxy, we bound the risk of the maximum likelihood estimator of network connections probabilities, and show that it is minimax optimal. Moreover, we show that our estimator can be efficiently approximated using tractable variational methods, and thus used in practice.