To refer to this page use:
|Abstract:||This paper considers the inverse problem with observed variables Y = BGX circle plus Z, where B-G is the incidence matrix of a graph G, X is the vector of unknown vertex variables with a uniform prior, and Z is a noise vector with Bernoulli (epsilon) i.i.d. entries. All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems. In particular, it corresponds to a stochastic block model or a correlation clustering problem with two communities and censored edges. Without noise, exact recovery of X is possible if and only the graph G is connected, with a sharp threshold at the edge probability log(n)/n for Erdos-Renyi random graphs. The first goal of this paper is to determine how the edge probability p needs to scale to allow exact recovery in the presence of noise. Defining the degree (oversampling) rate of the graph by alpha = np/log(n), it is shown that exact recovery is possible if and only if alpha > 2/(1 - 2 epsilon)(2) + o(1/(1 - 2 epsilon)(2)). In other words, 2/(1 - 2 epsilon)(2) is the information theoretic threshold for exact recovery at low-SNR. In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate. Full version available in .|
|Electronic Publication Date:||11-Aug-2014|
|Citation:||Abbe, Emmanuel, Bandeira, Afonso S, Bracher, Annina, Singer, Amit. (2014). Linear inverse problems on Erdos-Renyi graphs: Information-theoretic limits and efficient recovery. 2014 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 1251 - 1255|
|Pages:||1251 - 1255|
|Type of Material:||Conference Article|
|Journal/Proceeding Title:||2014 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)|
Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.