Bayes.FactorElimination

Algorithms for factor elimination

Moral graph

moralGraph :: (NamedGraph g, FoldableWithVertex g, DirectedGraph g) => g () b -> UndirectedSG () b

For the junction tree construction, only the vertices are needed during the intermediate steps. So, the moral graph is returned without any vertex data.

Triangulation

nodeComparisonForTriangulation :: (UndirectedGraph g, Factor f) => g a f -> Vertex -> Vertex -> Ordering

Node selection comparison function used for triangulating the graph

numberOfAddedEdges :: UndirectedGraph g => g a b -> Vertex -> Int

Number of edges added when connecting all neighbors

triangulate

Arguments

:: Graph g

=> (Vertex -> Vertex -> Ordering)

Criterion function for triangulation

-> g () b

-> ([VertexCluster], g () b)

Returns the clusters and the triangulated graph

Triangulate a graph using a cost function The result is the triangulated graph and the list of clusters which may not be maximal.

Junction tree

minimumSpanningTree :: UndirectedGraph g => g Int f -> Tree () f

Implementing the Prim's algorithm for minimum spanning tree

createClusterGraph :: UndirectedGraph g => [VertexCluster] -> g Int VertexCluster

Create the cluster graph

data Cluster

Cluster of discrete variables. Discrete variables instead of vertices are needed because the factor are using DV and we need to find which factors must be contained in a given cluster.

Instances

Eq Cluster

Show Cluster

createJunctionTree

Arguments

:: (DirectedGraph g, FoldableWithVertex g, NamedGraph g, Factor f, Show f)

=> (UndirectedSG () f -> Vertex -> Vertex -> Ordering)

Weight function on the moral graph

-> BayesianNetwork g f

Input directed graph

-> JunctionTree f

Junction tree

Create a function tree

type JunctionTree f = Tree (Separator f) (JTNodeValue f)

The junction tree

Shenoy-Shafer message passing

collect :: Factor f => JunctionTree f -> JunctionTree f

Collect phase of the junction tree

distribute :: Factor f => Maybe (Separator f) -> JunctionTree f -> JunctionTree f

Distribute phase of the junction tree

posterior :: Factor f => JunctionTree f -> DV -> Maybe f

Compute the marginal posterior (if some evidence is set on the junction tree) otherwise compute just the marginal prior.

Evidence

clearEvidence :: Factor f => JunctionTree f -> JunctionTree f

Remove evidence in the junction tree

updateEvidence :: Factor f => DVISet Int -> JunctionTree f -> JunctionTree f

Update evidence in the tree

Test

junctionTreeProperty_prop :: DirectedSG () String -> Property

createVerticesJunctionTree

Arguments

:: (DirectedGraph g, FoldableWithVertex g, NamedGraph g)

=> (UndirectedSG () b -> Vertex -> Vertex -> Ordering)

Weight function on the moral graph

-> g () b

Input directed graph

-> Tree () VertexCluster

Junction tree

Create a junction tree with only the clusters and no factors

data VertexCluster

A cluster containing only the vertices and not yet the factors

Instances

Eq VertexCluster

Show VertexCluster

Show (Tree () VertexCluster)