Related papers: Oracle inequalities for network models and sparse …
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 in-homogeneous random graph model with missing…
Block graphons (also called stochastic block models) are an important and widely-studied class of models for random networks. We provide a lower bound on the accuracy of estimators for block graphons with a large number of blocks. We show…
Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive…
We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical…
In the present paper we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities $\Lambda$ when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In…
We study low-rank estimation of an unknown sparse graphon from sampled network data under operator-norm loss, motivated by targeted interventions in graphon games. Starting from the observed adjacency matrix, we construct low-rank…
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…
Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network…
We study the optimal estimation of probability matrices of random graph models generated from graphons. This problem has been extensively studied in the case of step-graphons and H\"older smooth graphons. In this work, we characterize the…
We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern,…
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…
In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
Inspired by Kalikow-type decompositions, we introduce a new stochastic model of infinite neuronal networks, for which we establish sharp oracle inequalities for Lasso methods and restricted eigenvalue properties for the associated Gram…
We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms and analysis go beyond previous work in several…