Stochastic simulation
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Loopy Belief Propagation: Convergence and Effects of Message Errors
The Journal of Machine Learning Research
Dynamic quantization for belief propagation in sparse spaces
Computer Vision and Image Understanding
Motion Estimation via Belief Propagation
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
Support Vector Machines
Graphical Models, Exponential Families, and Variational Inference
Graphical Models, Exponential Families, and Variational Inference
Nonparametric belief propagation
Communications of the ACM
A Database and Evaluation Methodology for Optical Flow
International Journal of Computer Vision
PAMPAS: real-valued graphical models for computer vision
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Loopy belief propagation and Gibbs measures
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking
IEEE Transactions on Signal Processing
Convergence Analysis of Reweighted Sum-Product Algorithms
IEEE Transactions on Signal Processing
The generalized distributive law
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
Sufficient Conditions for Convergence of the Sum–Product Algorithm
IEEE Transactions on Information Theory
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The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing (SOSMP), for computing the BP fixed point in models with continuous random variables. It is based on a deterministic approximation of the messages via orthogonal series basis expansion, and a stochastic estimation of the basis coefficients via Monte Carlo techniques and damped updates. We prove that the SOSMP iterates converge to a δ-neighborhood of the unique BP fixed point for any tree-structured graph, and for any graphs with cycles in which the BP updates satisfy a contractivity condition. In addition, we demonstrate how to choose the number of basis coefficients as a function of the desired approximation accuracy δ and smoothness of the compatibility functions. We illustrate our theory with both simulated examples and in application to optical flow estimation.