Estimating matrix of connection probabilities is one of the key issues when studying sparse networks with missing observations. This problem has applications in various fields such as biology, sociology, but also recommender systems. However, many real networks are polluted by outliers coming from different sources such as fraudulent behavior of malicious users or faulty measurement instruments. The robustness of the methods against these outliers, as well as their identification, is therefore a crucial problem in network analysis.

In this talk, I will first recall classical results and methods in network estimation. In a second part, I will present a joint work with G. Robin and O. Klopp on outlier identification and robust estimation of networks in the presence of missing links. I will present a new algorithm for detecting outliers in a network that simultaneously predicts missing links. The proposed method is statistically sound and computationally efficient. Finally, I will illustrate the method with an application in epidemiology, and with the analysis of a political Twitter network.