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

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.

Overview of Sparse Graph for Multiple Access in Future Mobile Networks

Frequenz ◽  
2017 ◽  
Vol 71 (11-12) ◽  
Author(s):  
Jing Lei ◽  
Baoguo Li ◽  
Erbao Li ◽  
Zhenghui Gong
Keyword(s):  
Wireless Communications ◽  
Mobile Networks ◽  
Message Passing ◽  
Multiple Access ◽  
Low Density ◽  
Sparse Graph ◽  
Extrinsic Information ◽  
Promising Technique ◽  
Satisfactory Performance ◽  
Message Passing Algorithm

AbstractMultiple access via sparse graph, such as low density signature (LDS) and sparse code multiple access (SCMA), is a promising technique for future wireless communications. This survey presents an overview of the developments in this burgeoning field, including transmitter structures, extrinsic information transform (EXIT) chart analysis and comparisons with existing multiple access techniques. Such technique enables multiple access under overloaded conditions to achieve a satisfactory performance. Message passing algorithm is utilized for multi-user detection in the receiver, and structures of the sparse graph are illustrated in detail. Outlooks and challenges of this technique are also presented.

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.

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 Properties of Bethe Free Energies and Message Passing in Gaussian Models

2011 ◽  
Vol 41 ◽  
pp. 1-24 ◽  
Author(s):  
B. Cseke ◽  
T. Heskes
Keyword(s):  
Free Energy ◽  
Message Passing ◽  
Probabilistic Models ◽  
Mean Field ◽  
Necessary Condition ◽  
Free Energies ◽  
Gaussian Models ◽  
Message Passing Algorithm ◽  
Bethe Free Energy ◽  
The Moment

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Bethe free energy and establish a necessary condition for the lower bound to be bounded from below. It turns out that the condition is identical to the pairwise normalizability condition, which is known to be a sufficient condition for the convergence of the message passing algorithm. We show that stable fixed points of the Gaussian message passing algorithm are local minima of the Gaussian Bethe free energy. By a counterexample, we disprove the conjecture stating that the unboundedness of the free energy implies the divergence of the message passing algorithm.

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