Tree Graphical Model

The FactorGraph supports the composite type ContinuousTreeModel based on the forward–backward message passing schedule, with three fields:

• ContinuousTreeGraph;
• ContinuousInference;
• ContinuousSystem.

The subtype ContinuousTreeGraph describes the tree factor graph obtained based on the input data. The GBP inference and marginal values are kept in the subtype ContinuousInference. The system of the linear equations being solved is preserved in the subtype ContinuousSystem. Note that the function continuousTreeModel() returns the main composite type ContinuousTreeModel with all subtypes.

Build graphical model

Input arguments of the function continuousTreeModel() describe the tree graphical model, while the function returns ContinuousTreeModel type.

Loads the system data passing arguments:

gbp = continuousTreeModel(coefficient, observation, variances)

Virtual factor nodes

The function continuousTreeModel() receives arguments by keyword to set the mean and variance of the virtual factor nodes to initiate messages from leaf variable nodes if the corresponding variable node does not have a singly connected factor node.

gbp = continuousTreeModel(DATA; mean = value, variance = value)

Default setting of the mean value is mean = 0.0, while the default variance is equal to variance = 1e10.

Root variable node

The function continuousTreeModel() receives argument by keyword to set the root variable node.

gbp = continuousTreeModel(DATA; root = index)

Default setting of the root variable node is root = 1.

Tree factor graph

Function checks whether the factor graph has a tree structure.

tree = isTree(gbp)

The tree structure of tha factor graph is marked as tree = true, the opposite is tree = false. The function accepts the composite type ContinuousTreeModel, as well as the type ContinuousModel.