scholarly journals Recovering a hidden community beyond the Kesten–Stigum threshold in O(|E|log*|V|) time

2018 ◽  
Vol 55 (2) ◽  
pp. 325-352 ◽  
Author(s):  
Bruce Hajek ◽  
Yihong Wu ◽  
Jiaming Xu
Keyword(s):  
Message Passing ◽  
Belief Propagation ◽  
Linear Time ◽  
Signal To Noise Ratio ◽  
Bp Algorithm ◽  
Local Algorithm ◽  
Message Passing Algorithm ◽  
Edge Probability ◽  
Effective Signal ◽  
Total Time Complexity

Abstract Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the graph G, with o(K) misclassified vertices on average, in the sublinear regime n1-o(1) ≤ K ≤ o(n). A critical parameter is the effective signal-to-noise ratio λ = K2(p - q)2 / ((n - K)q), with λ = 1 corresponding to the Kesten–Stigum threshold. We show that a belief propagation (BP) algorithm achieves weak recovery if λ > 1 / e, beyond the Kesten–Stigum threshold by a factor of 1 / e. The BP algorithm only needs to run for log*n + O(1) iterations, with the total time complexity O(|E|log*n), where log*n is the iterated logarithm of n. Conversely, if λ ≤ 1 / e, no local algorithm can asymptotically outperform trivial random guessing. Furthermore, a linear message-passing algorithm that corresponds to applying a power iteration to the nonbacktracking matrix of the graph is shown to attain weak recovery if and only if λ > 1. In addition, the BP algorithm can be combined with a linear-time voting procedure to achieve the information limit of exact recovery (correctly classify all vertices with high probability) for all K ≥ (n / logn) (ρBP + o(1)), where ρBP is a function of p / q.

scholarly journals Cooperative Localization for Mobile Networks: A Distributed Belief Propagation–Mean Field Message Passing Algorithm

2016 ◽  
Vol 23 (6) ◽  
pp. 828-832 ◽  
Author(s):  
Burak Cakmak ◽  
Daniel N. Urup ◽  
Florian Meyer ◽  
Troels Pedersen ◽  
Bernard H. Fleury ◽  
...  
Keyword(s):  
Mobile Networks ◽  
Message Passing ◽  
Belief Propagation ◽  
Mean Field ◽  
Cooperative Localization ◽  
Message Passing Algorithm

scholarly journals Analysis of TDMP Algorithm of LDPC Codes Based on Density Evolution and Gaussian Approximation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 457 ◽  
Author(s):  
Xiumin Wang ◽  
Hong Chang ◽  
Jun Li ◽  
Weilin Cao ◽  
Liang Shan
Keyword(s):  
Message Passing ◽  
Belief Propagation ◽  
Gaussian Approximation ◽  
Bp Algorithm ◽  
Turbo Decoding ◽  
Density Evolution ◽  
Analysis Process ◽  
Evolution Analysis ◽  
Simplified Algorithm ◽  
Previous Iteration

Based on density evolution analysis of the existing belief propagation (BP) algorithm, the Turbo Decoding Message Passing (TDMP) algorithm was analyzed from the perspective of density evolution and Gaussian approximation, and the theoretical analysis process of TDMP algorithm was given. When calculating the prior message of each layer of the TDMP algorithm, the check message of the previous iteration should be subtracted. Therefore, the result will not be convergent, if the TDMP algorithm is directly analyzed based on density evolution and Gaussian approximation. We researched the TDMP algorithm based on the symmetry conditions to obtain the convergent result. When using density evolution (DE) and Gaussian approximation to analyze the decoding convergence of the TDMP algorithm, we can provide a theoretical basis for proving the superiority of the algorithm. Then, based on the DE theory, we calculated the probability density function (PDF) of the check-to-variable information of TDMP and its simplified algorithm, and then gave it a calculation based on the process of the normalization factor. Simulation results show that the decoding convergence speed of the TDMP algorithm was faster and the iterations were smaller compared to the BP algorithm under the same conditions.

Efficient nonparametric belief propagation for pose estimation and manipulation of articulated objects

2019 ◽  
Vol 4 (30) ◽  
pp. eaaw4523 ◽  
Author(s):  
Karthik Desingh ◽  
Shiyang Lu ◽  
Anthony Opipari ◽  
Odest Chadwicke Jenkins
Keyword(s):  
Pose Estimation ◽  
Message Passing ◽  
Belief Propagation ◽  
Sensor Data ◽  
Depth Sensor ◽  
Continuous Space ◽  
Articulated Objects ◽  
Message Passing Algorithm ◽  
Wide Range ◽  
Object Part

Robots working in human environments often encounter a wide range of articulated objects, such as tools, cabinets, and other jointed objects. Such articulated objects can take an infinite number of possible poses, as a point in a potentially high-dimensional continuous space. A robot must perceive this continuous pose to manipulate the object to a desired pose. This problem of perception and manipulation of articulated objects remains a challenge due to its high dimensionality and multimodal uncertainty. Here, we describe a factored approach to estimate the poses of articulated objects using an efficient approach to nonparametric belief propagation. We consider inputs as geometrical models with articulation constraints and observed RGBD (red, green, blue, and depth) sensor data. The described framework produces object-part pose beliefs iteratively. The problem is formulated as a pairwise Markov random field (MRF), where each hidden node (continuous pose variable) is an observed object-part’s pose and the edges denote the articulation constraints between the parts. We describe articulated pose estimation by a “pull” message passing algorithm for nonparametric belief propagation (PMPNBP) and evaluate its convergence properties over scenes with articulated objects. Robot experiments are provided to demonstrate the necessity of maintaining beliefs to perform goal-driven manipulation tasks.

scholarly journals A Spectral Approach to Analysing Belief Propagation for 3-Colouring

2009 ◽  
Vol 18 (6) ◽  
pp. 881-912 ◽  
Author(s):  
AMIN COJA-OGHLAN ◽  
ELCHANAN MOSSEL ◽  
DAN VILENCHIK
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Graphical Model ◽  
Belief Propagation ◽  
Graph Colouring ◽  
Rigorous Result ◽  
Theoretical Understanding ◽  
Message Passing Algorithm ◽  
Survey Propagation ◽  
Graphical Structure

Belief propagation (BP) is a message-passing algorithm that computes the exact marginal distributions at every vertex of a graphical model without cycles. While BP is designed to work correctly on trees, it is routinely applied to general graphical models that may contain cycles, in which case neither convergence, nor correctness in the case of convergence is guaranteed. Nonetheless, BP has gained popularity as it seems to remain effective in many cases of interest, even when the underlying graph is ‘far’ from being a tree. However, the theoretical understanding of BP (and its new relative survey propagation) when applied to CSPs is poor.Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ‘planted’ solution; thus, we obtain the first rigorous result on BP for graph colouring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how belief propagation breaks the symmetry between the 3! possible permutations of the colour classes.

A Novel LLR-BP Algorithm for LDPC Codes Based on Taylor Series and Least Squares

2013 ◽  
Vol 462-463 ◽  
pp. 193-197
Author(s):  
Xing Ru Zhang ◽  
Jian Ping Li ◽  
Chao Shi Cai
Keyword(s):  
Least Squares ◽  
Taylor Series ◽  
Belief Propagation ◽  
Signal To Noise Ratio ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Significant Loss ◽  
Bp Algorithm ◽  
High Signal ◽  
Decoding Algorithm

An effective log-likelihood-ratio-based belief propagation (LLR-BP) algorithm is proposed. It can reduce computational complexity of decoding algorithm for Low Density Parity Check (LDPC) codes. By using the Taylor series and least squares, high order multiplication based on the hyperbolic tangent (tanh) rule is converted to a first-order multiplication and addition after simplification. Moreover, all the logarithmic and exponential operations disappear without significant loss of the decoding performance. The simulation results show that the performance of the proposed scheme is similar to the general LLR-BP. In particular, we show that the modified algorithm with low complexity can achieve better BER than the other decoding algorithm in high signal-to-noise ratio region.

Research on LIFT Technology for 3D Seismic Denoising in Coalfield

2014 ◽  
Vol 556-562 ◽  
pp. 6328-6331
Author(s):  
Su Zhen Shi ◽  
Yi Chen Zhao ◽  
Li Biao Yang ◽  
Yao Tang ◽  
Juan Li
Keyword(s):  
Signal To Noise Ratio ◽  
High Signal ◽  
3D Seismic ◽  
Signal To Noise ◽  
Denoising Method ◽  
Seismic Processing ◽  
Work Area ◽  
Noise Data ◽  
Noise Ratio ◽  
Effective Signal

The LIFT technology has applied in process of denoising to ensure the imaging precision of minor faults and structure in 3D coalfield seismic processing. The paper focused on the denoising process in two study areas where the LIFT technology is used. The separation of signal and noise is done firstly. Then denoising would be done in the noise data. The Data of weak effective signal that is from the noise data could be blended with the original effective signal to reconstruct the denoising data, so the result which has high signal-to-noise ratio and preserved amplitude is acquired. Thus the fact shows that LIFT is an effective denoising method for 3D seismic in coalfield and could be used widely in other work area.

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