Mathematical structures of loopy belief propagation and cluster variation method

Mathematical structures of loopy belief propagation and cluster variation method

The mathematical structures of loopy belief propagation are reviewed for graphical models in probabilistic information processing in the stand point of cluster variation method. An extension of adaptive TAP approaches is given by introducing a generalized scheme of the cluster variation method. Moreover the practical message update rules in loopy belief propagation are summarized also for quant...

Hybrid Loopy Belief Propagation

We propose an algorithm called Hybrid Loopy Belief Propagation (HLBP), which extends the Loopy Belief Propagation (LBP) (Murphy et al., 1999) and Nonparametric Belief Propagation (NBP) (Sudderth et al., 2003) algorithms to deal with general hybrid Bayesian networks. The main idea is to represent the LBP messages with mixture of Gaussians and formulate their calculation as Monte Carlo integratio...

Loopy Belief Propagation Algorithm

check the effectiveness. In some cases, such as Dobrushin's condition is satisfied, the error bounds and the improvement procedure seem effective. Nevertheless, the region where one can obtain good bounds seems restrictive. We give some remarks in the rest of this section. First, the concept of estimates we used in this paper was developed for general Gibbs measures, so that there may be a poss...

Loopy Belief Propagation and Gibbs Measures

Loopy belief propagation and probabilistic image processing

The hyperparameter estimation in the maximization of the marginal likelihood in the probabilistic image processing is investigated by using the cluster variation method. The algorithms are substantially equivalent to generalized loopy belief propagations.