fglib
The factor graph library (fglib) is a Python package to simulate message passing on factor graphs. It supports the
 sumproduct algorithm (belief propagation)
 maxproduct algorithm
 maxsum algorithm
 meanfield algorithm  in development
with discrete and Gaussian random variables.
Installation
Install fglib with the Python Package Index by using
pip install fglib
Install fglib with setuptools by using
python setup.py install
Dependencies
 Python 3.4 or later
 NetworkX 2.0 or later
 NumPy 1.12 or later
 matplotlib 2.0 or later
Documentation
In order to generate the documentation site for the factor graph library, execute the following commands from the toplevel directory.
$ cd docs/
$ make html
Example
Examples (like the following one) are located in the examples/
directory.
"""A simple example of the sumproduct algorithm
This is a simple example of the sumproduct algorithm on a factor graph
with Discrete random variables.
/\ ++ /\ ++ /\
 x1  fa  x2  fb  x3 
\/ ++ \/ ++ \/

++
 fc 
++

/\
 x4 
\/
The following joint distributions are used for the factor nodes.
fa  x2=0 x2=1 x2=2 fb  x3=0 x3=1 fc  x4=0 x4=1
  
x1=0  0.3 0.2 0.1 x2=0  0.3 0.2 x2=0  0.3 0.2
x1=1  0.3 0.0 0.1 x2=1  0.3 0.0 x2=1  0.3 0.0
x2=2  0.1 0.1 x2=2  0.1 0.1
"""
from fglib import graphs, nodes, inference, rv
# Create factor graph
fg = graphs.FactorGraph()
# Create variable nodes
x1 = nodes.VNode("x1", rv.Discrete) # with 2 states (Bernoulli)
x2 = nodes.VNode("x2", rv.Discrete) # with 3 states
x3 = nodes.VNode("x3", rv.Discrete)
x4 = nodes.VNode("x4", rv.Discrete)
# Create factor nodes (with joint distributions)
dist_fa = [[0.3, 0.2, 0.1],
[0.3, 0.0, 0.1]]
fa = nodes.FNode("fa", rv.Discrete(dist_fa, x1, x2))
dist_fb = [[0.3, 0.2],
[0.3, 0.0],
[0.1, 0.1]]
fb = nodes.FNode("fb", rv.Discrete(dist_fb, x2, x3))
dist_fc = [[0.3, 0.2],
[0.3, 0.0],
[0.1, 0.1]]
fc = nodes.FNode("fc", rv.Discrete(dist_fc, x2, x4))
# Add nodes to factor graph
fg.set_nodes([x1, x2, x3, x4])
fg.set_nodes([fa, fb, fc])
# Add edges to factor graph
fg.set_edge(x1, fa)
fg.set_edge(fa, x2)
fg.set_edge(x2, fb)
fg.set_edge(fb, x3)
fg.set_edge(x2, fc)
fg.set_edge(fc, x4)
# Perform sumproduct algorithm on factor graph
# and request belief of variable node x4
belief = inference.sum_product(fg, x4)
# Print belief of variables
print("Belief of variable node x4:")
print(belief)
References

B. J. Frey, F. R. Kschischang, H.A. Loeliger, and N. Wiberg, "Factor graphs and algorithms," in Proc. 35th Allerton Conf. Communications, Control, and Computing, Monticello, IL, Sep. 29Oct. 1, 1997, pp. 666680.

F. R. Kschischang, B. J. Frey, and H.A. Loeliger, “Factor graphs and the sumproduct algorithm,” IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 498–519, Feb. 2001.

H.A. Loeliger, “An introduction to factor graphs,” IEEE Signal Process. Mag., vol. 21, no. 1, pp. 28–41, Jan. 2004.

H.A. Loeliger, J. Dauwels, H. Junli, S. Korl, P. Li, and F. R. Kschischang, “The factor graph approach to modelbased signal processing,” Proc. IEEE, vol. 95, no. 6, pp. 1295–1322, Jun. 2007.

H. Wymeersch, Iterative Receiver Design. Cambridge, UK: Cambridge University Press, 2007.

C. M. Bishop, Pattern Recognition and Machine Learning, 8th ed., ser. Information Science and Statistics. New York, USA: Springer Science+Business Media, 2009.