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I. Naïve Belief Propagation Algorithm
"... One of the greatest abilities of the human eye is its capacity to perceive depth, an essential skill that allows us to perform fundamental tasks, such as avoiding obstacles and retrieving objects, as well as complicated tasks, such as driving a car. As advancements in the field of robotics allow rob ..."
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, introduced by Pedro Felzenszwalb of the University of Chicago, were applied to a naïve belief propagation algorithm to achieve more efficient belief propagation in depth finding. This paper provides an overview of the naïve belief propagation algorithm, the algorithm optimizations, and experimental results
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
- IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems
Turbo decoding as an instance of Pearl’s belief propagation algorithm
- IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pear ..."
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Cited by 404 (16 self)
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: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network ” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his
Implementing the Belief Propagation Algorithm in MATLAB
, 2008
"... We provide some example Matlab code as a supplement to the paper [6]. This technical report is not intended as a standalone introduction to the belief propagation algorithm, but instead only aims to provide some technical material, which didn’t fit into the paper. 1 ..."
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We provide some example Matlab code as a supplement to the paper [6]. This technical report is not intended as a standalone introduction to the belief propagation algorithm, but instead only aims to provide some technical material, which didn’t fit into the paper. 1
The serial and parallel belief propagation algorithms
- in Proc. IEEE Intern. Symp. on Inform. Theory
"... Abstract — It has been shown that the stable fixed points of belief propagation (BP) algorithms correspond to extrema of the Bethe free energy. In this paper, we describe the dual problem for the minimization of the Bethe free energy and solve it using simple nonlinear block Gauss-Seidel and Jacobi ..."
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Cited by 1 (0 self)
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Abstract — It has been shown that the stable fixed points of belief propagation (BP) algorithms correspond to extrema of the Bethe free energy. In this paper, we describe the dual problem for the minimization of the Bethe free energy and solve it using simple nonlinear block Gauss-Seidel and Jacobi
On Robust Stability of the Belief Propagation Algorithm for LDPC Decoding
"... Abstract — The exact nonlinear loop gain of the belief propagation algorithm (BPA) in its log-likelihood ratio (LLR) formulation is computed. The nonlinear gains for regular lowdensity parity-check (LDPC) error correcting codes can be computed exactly using a simple formula. It is shown that in some ..."
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Cited by 2 (1 self)
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Abstract — The exact nonlinear loop gain of the belief propagation algorithm (BPA) in its log-likelihood ratio (LLR) formulation is computed. The nonlinear gains for regular lowdensity parity-check (LDPC) error correcting codes can be computed exactly using a simple formula. It is shown
On the Optimality of Solutions of the Max-Product Belief Propagation Algorithm in Arbitrary Graphs
, 2001
"... Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The max-product "belief propagation" algorithm is a local-message passing algorithm on this graph that is known to converge to a unique fixed point when the gra ..."
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Cited by 241 (13 self)
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Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The max-product "belief propagation" algorithm is a local-message passing algorithm on this graph that is known to converge to a unique fixed point when
On the Convergence of Belief Propagation Algorithm for Stochastic Networks With Loops
, 2004
"... The belief propagation (BP) algorithm is a tool with which one can calculate beliefs, marginal probabilities, of stochastic networks without loops (e.g., Bayesian networks) in a time proportional to the number of nodes. For networks with loops, it may not converge and, even if it converges, beliefs ..."
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The belief propagation (BP) algorithm is a tool with which one can calculate beliefs, marginal probabilities, of stochastic networks without loops (e.g., Bayesian networks) in a time proportional to the number of nodes. For networks with loops, it may not converge and, even if it converges, beliefs
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169,865
