Related papers: Recovery thresholds in the sparse planted matching…
Motivated by applications such as discovering strong ties in social networks and assembling genome subsequences in biology, we study the problem of recovering a hidden $2k$-nearest neighbor (NN) graph in an $n$-vertex complete graph, whose…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
We study the fundamental limits for reconstruction in weighted graph (or matrix) database alignment. We consider a model of two graphs where $\pi^*$ is a planted uniform permutation and all pairs of edge weights $(A_{i,j},…
Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex…
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured…
We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the integers that is assumed to be invariant under index shifts…
To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…
Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on…
In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
The problem of aligning Erd\"os-R\'enyi random graphs is a noisy, average-case version of the graph isomorphism problem, in which a pair of correlated random graphs is observed through a random permutation of their vertices. We study a…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
This paper considers the problem of label recovery in random graphs and matrices. Motivated by transitive behavior in real-world networks (i.e., ``the friend of my friend is my friend''), a recent line of work considers spatially-embedded…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying "true" statistical models. To address this issue, we take a first step towards taming model misspecification by…