SymbolicBayesTree - GTSAM Docs

A SymbolicBayesTree is a tree structure where each node (SymbolicBayesTreeClique) represents a clique of variables that were eliminated together during multifrontal elimination. Unlike a SymbolicJunctionTree which stores factors, a SymbolicBayesTree stores the resulting SymbolicConditional for each clique.

It represents the factored structure $P(X) = Π P(C_j | S_j)$ , where $C_j$ are the frontal variables of clique $j$ and $S_j$ are its separator variables (parents in the Bayes Tree). This structure is computationally advantageous for inference, especially for calculating marginals or performing incremental updates (like in iSAM).

from gtsam import SymbolicFactorGraph, Ordering
from gtsam.symbol_shorthand import X, L
import graphviz # For visualization

Creating a SymbolicBayesTree¶

A Bayes tree is typically created by eliminating a SymbolicFactorGraph using the multifrontal method.

# Create a factor graph from a GTSFM problem
graph = SymbolicFactorGraph()

edges = [(2, 4), (2, 5), (2, 27), (4, 6), (5, 6), (5, 7), (5, 8), (5, 9), (6, 7), (6, 8), (6, 9), 
         (7, 8), (7, 9), (8, 9), (9, 12), (9, 24), (9, 28), (10, 12), (10, 29), (20, 21), (20, 22), 
         (20, 23), (20, 24), (21, 22), (21, 23), (21, 24), (22, 23), (22, 24), (23, 24), (25, 26), 
         (25, 27), (25, 28), (25, 29), (26, 27), (26, 28), (26, 29), (27, 28), (27, 29), (28, 29)]

for i,j in edges:
    graph.push_factor(X(i), X(j))

# Define an elimination ordering
ordering = Ordering.MetisSymbolicFactorGraph(graph)  # Use METIS for this example

# Eliminate using Multifrontal method
bayes_tree = graph.eliminateMultifrontal(ordering)

Visualization and Properties¶

The Bayes tree structure can be visualized, and we can query its properties.

print(f"\nBayes Tree size (number of cliques): {bayes_tree.size()}")
print(f"Is the Bayes Tree empty? {bayes_tree.empty()}")


Bayes Tree size (number of cliques): 8
Is the Bayes Tree empty? False

# Visualize the Bayes tree using graphviz
display(graphviz.Source(bayes_tree.dot()))

Traversing a Bayes Tree¶

roots = bayes_tree.roots()
print(f"Number of roots: {len(roots)}")

def traverse_clique(clique):
    if clique:
        clique.print("\nClique:\n")
        for j in range(clique.nrChildren()):
            traverse_clique(clique[j])

for root in roots:
    traverse_clique(root)

Number of roots: 1

Clique:
 P( x28 x25 x26 x9 x29 x27)

Clique:
 P( x5 x4 | x9 x27)

Clique:
 P( x2 | x4 x5 x27)

Clique:
 P( x6 | x4 x5 x9)

Clique:
 P( x8 x7 | x5 x6 x9)

Clique:
 P( x12 | x9 x29)

Clique:
 P( x10 | x12 x29)

Clique:
 P( x24 x23 x22 x21 x20 | x9)

GTSAM Docs

SymbolicBayesTreeClique

GTSAM Docs

SymbolicConditional