相关论文: Information Limits for Recovering a Hidden Communi…

We consider the problem of community detection or clustering in the labeled Stochastic Block Model (LSBM) with a finite number $K$ of clusters of sizes linearly growing with the global population of items $n$. Every pair of items is labeled…

The stochastic block model (SBM) is an important generative model for random graphs in network science and machine learning, useful for benchmarking community detection (or clustering) algorithms. The symmetric SBM generates a graph with…

We study the weak recovery problem on the $r$-uniform hypergraph stochastic block model ($r$-HSBM) with two balanced communities. In this model, $n$ vertices are randomly divided into two communities, and size-$r$ hyperedges are added…

A fundamental theoretical question in network analysis is to determine under which conditions community recovery is possible in polynomial time in the Stochastic Block Model (SBM). When the number $K$ of communities remains smaller than…

We study information theoretic limits of recovering an unknown $n$ dimensional, complex signal vector $\mathbf{x}_\star$ with unit norm from $m$ magnitude-only measurements of the form $y_i = |(\mathbf{A} \mathbf{x}_\star)_i|^2, \; i = 1,2…

We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity". Specifically, we consider $m\times n$ random matrices…

We address the problem of variable selection in a high-dimensional but sparse mean model, under the additional constraint that only privatised data are available for inference. The original data are vectors with independent entries having a…

A variety of information processing tasks in practice involve recovering $n$ objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph $\mathcal{G}$. This paper concerns the…

Multi-view data arises frequently in modern network analysis e.g. relations of multiple types among individuals in social network analysis, longitudinal measurements of interactions among observational units, annotated networks with noisy…

Consider a query-based data acquisition problem that aims to recover the values of $k$ binary variables from parity (XOR) measurements of chosen subsets of the variables. Assume the response model where only a randomly selected subset of…

Given a large data matrix $A\in\mathbb{R}^{n\times n}$, we consider the problem of determining whether its entries are i.i.d. with some known marginal distribution $A_{ij}\sim P_0$, or instead $A$ contains a principal submatrix $A_{{\sf…

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…

We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic…

Due to the recent development of data analysis techniques, technologies for detecting communities through information expressed in social networks have been developed. Although it has several advantages, including the ability to effectively…

The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…

The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users (represented by adjacency matrix of a graph). There has been significant…

The problem central to sparse recovery and compressive sensing is that of stable sparse recovery: we want a distribution of matrices A in R^{m\times n} such that, for any x \in R^n and with probability at least 2/3 over A, there is an…

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden…

We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying ||x-x'||_1 <= C min_{k-sparse} x"} ||x-x"||_1. It is known that there exist…

We study the problem of $\textit{robust community recovery}$: efficiently recovering communities in sparse stochastic block models in the presence of adversarial corruptions. In the absence of adversarial corruptions, there are efficient…