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Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…

We study the mixing properties of the single-site Markov chain known as the Glauber dynamics for sampling $k$-colorings of a sparse random graph $G(n,d/n)$ for constant $d$. The best known rapid mixing results for general graphs are in…

A sequential test is proposed for detection and isolation of hubs in a correlation graph. Hubs in a correlation graph of a random vector are variables (nodes) that have a strong correlation edge. It is assumed that the random vectors are…

The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…

Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…

Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled…

In many applications, training machine learning models involves using large amounts of human-annotated data. Obtaining precise labels for the data is expensive. Instead, training with weak supervision provides a low-cost alternative. We…

This study addresses the issue of balancing graph summarization and graph change detection. Graph summarization compresses large-scale graphs into a smaller scale. However, the question remains: To what extent should the original graph be…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

We study graph bootstrap percolation on the Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$. For all $r \ge 5$, we locate the sharp $K_r$-percolation threshold $p_c \sim (\gamma n)^{-1/\lambda}$, solving a problem of Balogh, Bollob\'as…

We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection…

We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…

The use of tools from analysis to approach problems in graph theory has become an active area of research. Usually such methods are applied to problems involving dense graphs and hypergraphs; here we give the an extension of such methods to…

We consider the problem of fault tolerance in the graph-state model of quantum computation. Using the notion of composable simulations, we provide a simple proof for the existence of an accuracy threshold for graph-state computation by…

Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. Theoretically, an unknown signal with block structure can be accurately recovered from a few number of…

Beta decay is a fundamental process that governs nuclear stability and serves as a sensitive probe of the weak interaction and possible physics beyond the Standard Model of particle physics. However, precise measurements of complete $\beta$…

We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…

In this paper, we study community detection when we observe $m$ sparse networks and a high dimensional covariate matrix, all encoding the same community structure among $n$ subjects. In the asymptotic regime where the number of features $p$…

We prove that for every $\epsilon>0$ there exists $\delta>0$ such that the following holds. Let $\mathcal{C}$ be a collection of $n$ curves in the plane such that there are at most $(\frac{1}{4}-\epsilon)\frac{n^{2}}{2}$ pairs of curves…

Subspace tracking is a fundamental problem in signal processing, where the goal is to estimate and track the underlying subspace that spans a sequence of data streams over time. In high-dimensional settings, data samples are often corrupted…