Rate-optimal graphon estimation

Rate - Optimal Graphon Estimation

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with k clu...

Dynamic network models and graphon estimation

In the present paper we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities Λ when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In particular, in the context of DSBM, we derive penalized least squares estimator Λ̂ of Λ and show that Λ̂ satisfies an oracle inequality and also attains minimax lower bo...

Private Graphon Estimation for Sparse Graphs

We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph G, our algorithms output a node-differentially private nonparametric block model approximation. By node-differentially private, we mean that our output hides the insertion or removal of a vertex and all its adj...

Multi-rate optimal state estimation

Rates of Convergence of Spectral Methods for Graphon Estimation

This paper studies the problem of estimating the grahpon model – the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in recommender systems. The graphon model deals with a random graph of n vertices such that each pair of two vertices i and j are connected independently with p...