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. When risk is measured in Frobenius norm, no estimator running in polynomial time has been shown to attain the minimax optimal rate of convergence for this problem. Thus, maximum likelihood estimation is of particular interest as computationally efficient approximations to it have been proposed in the literature and are often used in practice.

Estimation of Dynamic Networks for High-Dimensional Nonstationary Time Series

“…This assumption is quite restrictive in practice and hardly plausible for many real-world applications such as gene regulatory networks, social networks, and stocking market, where the underlying data generating mechanisms are often dynamic. On the other hand, dynamic random networks have been extensively studied from the perspective of large random graphs such as community detection and edge probability estimation for dynamic stochastic block models (DSBMs) [39,50,33,16,24,23,31,19,21,48,49,8,5,30].…”

Graphon Estimation from Partially Observed Network Data

“…Recently, graphon estimation under a missing data set-up where one observes full ego-networks of some (but not all) individuals in a network has been carried out in Wu et al (2018). In general, the problem of link prediction with partially observed data has been tackled before in Zhao et al (2017); Gaucher and Klopp (2019).…”