Related papers: Optimal Recovery of Block Models with $q$ Communit…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances…
We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
We show that a simple community detection algorithm originated from stochastic blockmodel literature achieves consistency, and even optimality, for a broad and flexible class of sparse latent space models. The class of models includes…
We consider the problem of community detection from observed interactions between individuals, in the context where multiple types of interaction are possible. We use labelled stochastic block models to represent the observed data, where…
The problem of community detection receives great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…
This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not…
We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two community structure where the initial set of informed nodes lies only in one of the…
The problem of population recovery refers to estimating a distribution based on incomplete or corrupted samples. Consider a random poll of sample size $n$ conducted on a population of individuals, where each pollee is asked to answer $d$…
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. M\'ezard [Eur. Phys. B. 57, 175…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model builds on the random geometric graphs…
We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…
In an extant population, how much information do extant individuals provide on the pedigree of their ancestors? Recent work by Kim, Mossel, Ramnarayan and Turner (2020) studied this question under a number of simplifying assumptions,…
Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML)…