
Recovering a Hidden Community Beyond the Spectral Limit in O(E ^*V) Time
Community detection is considered for a stochastic block model graph of ...
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A Message Passing based Adaptive PDA Algorithm for Robust Radiobased Localization and Tracking
We present a message passing algorithm for localization and tracking in ...
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Robust Group Synchronization via CycleEdge Message Passing
We propose a general framework for group synchronization with adversaria...
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Statistical and computational thresholds for the planted kdensest subhypergraph problem
Recovery a planted signal perturbed by noise is a fundamental problem in...
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Inference via Message Passing on Partially Labeled Stochastic Block Models
We study the community detection and recovery problem in partiallylabel...
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Rankone matrix estimation with groupwise heteroskedasticity
We study the problem of estimating a rankone matrix from Gaussian obser...
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Information Limits for Recovering a Hidden Community
We study the problem of recovering a hidden community of cardinality K f...
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Submatrix localization via message passing
The principal submatrix localization problem deals with recovering a K× K principal submatrix of elevated mean μ in a large n× n symmetric matrix subject to additive standard Gaussian noise. This problem serves as a prototypical example for community detection, in which the community corresponds to the support of the submatrix. The main result of this paper is that in the regime Ω(√(n)) ≤ K ≤ o(n), the support of the submatrix can be weakly recovered (with o(K) misclassification errors on average) by an optimized message passing algorithm if λ = μ^2K^2/n, the signaltonoise ratio, exceeds 1/e. This extends a result by Deshpande and Montanari previously obtained for K=Θ(√(n)). In addition, the algorithm can be extended to provide exact recovery whenever informationtheoretically possible and achieve the information limit of exact recovery as long as K ≥n/ n (1/8e + o(1)). The total running time of the algorithm is O(n^2 n). Another version of the submatrix localization problem, known as noisy biclustering, aims to recover a K_1× K_2 submatrix of elevated mean μ in a large n_1× n_2 Gaussian matrix. The optimized message passing algorithm and its analysis are adapted to the bicluster problem assuming Ω(√(n_i)) ≤ K_i ≤ o(n_i) and K_1 K_2. A sharp informationtheoretic condition for the weak recovery of both clusters is also identified.
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