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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Abbe, E. Bandeira, A.S. Bracher, A. Singer, A. |
| Copyright Year | 2014 |
| Description | Author affiliation: Princeton Univ., Princeton, NJ, USA (Abbe, E.; Bandeira, A.S.; Bracher, A.; Singer, A.) |
| Abstract | This paper considers the inverse problem with observed variables Y = $B_{G}X$ ⊕ 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(ε) 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 Erdös-Rényi 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 α = np= log(n), it is shown that exact recovery is possible if and only if α > $2/(1-2ε)^{2}+o(1/(1-2ε)^{2}).$ In other words, $2/(1-2ε)^{2}$ 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 [1]. |
| Starting Page | 1251 |
| Ending Page | 1255 |
| File Size | 464406 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781479951864 |
| ISSN | 21578117 |
| DOI | 10.1109/ISIT.2014.6875033 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2014-06-29 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Noise Communities Synchronization Vectors Information theory Inverse problems Stochastic processes |
| Content Type | Text |
| Resource Type | Article |
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