Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node (or variable), conditional on any observed nodes (or variables).

This tutorial introduces belief propagation in the context of factor graphs and demonstrates its use in a simple model of stereo matching used in computer vision.

BELIEF PROPAGATION {ch:BP} Consider the ubiquitous problem of computing marginals of a graphical model with N variables x= (x1,...,xN) taking values in a finite alphabet X. The naive algorithm, summing over all configurations, takes a time of order |X|N. The complexity can be reduced dramatically when the underlying factor graph

potentials. This procedure is referred to as loopy belief propagation. While mathe­ matically unsound at a first glance, loopy BP performs surprisingly well on numerous real-world problems. On the flip side, loopy BP can also fail spectacularly, yielding nonsensical marginal distributions for certain problems. We want to figure out why

Belief propagation lets us efficiently estimate the states of unobserved variables in the system, for example, given these image observations, what is my estimate of the pose of the person?

Belief propagation (BP) is an algorithm for marginal inference, i.e. it computes the marginal posterior distribution for each variable from the set of factors that make up the joint posterior. BP is intimately linked to factor graphs by the following property: BP can be implemented as iterative message passing on the posterior factor graph .

We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing lo- cal messages.

2024年9月30日 · However, inference and learning in the models we want often poses a serious computational challenge. Belief propagation (BP) and its variants provide an attractive approximate solution, especially using recent training methods.

25.2 Belief Propagation and Inference in Graphical Models The message passing decoding algorithm for LDPC codes is an instantiation of a more general algorithm, known as belief propagation, that is used for inference in graphical models.

BELIEF PROPAGATION ! BP is a message passing algorithm that solves approxi mate inference problems in graphical model, including Bayesian networks and Markov random fields. ! Calculates marginal distribution for each of the unobs erved variable, conditional on any observed variables. ! It was first proposed by Judea Pearl in 1982 for trees