Related papers: Mutual information for the sparse stochastic block…

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data…

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…

The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…

In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…

We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…

A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be…

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…

In communications, unknown variables are usually modelled as random variables, and concepts such as independence, entropy and information are defined in terms of the underlying probability distributions. In contrast, control theory often…

We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…

We use a well known model (T. Vicsek et al. Phys Rev Lett 15, 1226 (1995)) for flocking to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that…

New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the…

The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the…

We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many…

The analysis of stochastic loss networks has long been of interest in computer and communications networks and is becoming important in the areas of service and information systems. In traditional settings, computing the well known Erlang…

The paper discusses a statistical problem related to testing for differences between two sparse networks with community structures. The community-wise edge probability matrices have entries of order $O(n^{-1}/\log n)$, where $n$ represents…

We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…

This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…

Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of…

Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector. We address the question of how long the…

This paper provides a selective review of the statistical network analysis literature focused on clustering and inference problems for stochastic blockmodels and their variants. We survey asymptotic normality results for stochastic…