Super-node normalized belief propagation for probabilistic systems

摘要

A method determines the probabilities of states of a system represented by a model including of nodes connected by links. Each node represents possible states of a corresponding part of the system, and each link represents statistical dependencies between possible states of related nodes. The nodes are grouped into arbitrary sized clusters such that every node is included in at least one cluster. A minimal number of marginalization constraints to be satisfied between the clusters are determined. A super-node network is constructed so that each cluster of nodes is represented by exactly one super-node. Super-nodes that share one of the marginalization constraints are connected by super-links. The super-node network is searched to locate closed loops of super-nodes containing at least one common node. A normalization operator for each closed loop is determined, and messages between the super-nodes are defined. Initial values are assigned to the messages, and the messages between super-nodes are updated using standard belief propagation. The messages are replaced by associated normalized values using the corresponding normalization operator, and approximate probabilities of the states of the system are determined from the messages when a termination condition is reached.