The factor graph library (fglib) is a Python package to simulate message passing on factor graphs. It supports the
- sum-product algorithm (belief propagation)
- max-product algorithm
- max-sum algorithm
- mean-field algorithm - in development
with discrete and Gaussian random variables.
Install fglib with the Python Package Index by using
pip install fglib
Install fglib with setuptools by using
python setup.py install
- Python 3.4 or later
- NetworkX 2.0 or later
- NumPy 1.14 or later
- matplotlib 2.0 or later
In order to generate the documentation site for the factor graph library, execute the following commands from the top-level directory.
$ cd docs/
$ make html
Examples (like the following one) are located in the examples/ directory.
"""A simple example of the sum-product algorithm
This is a simple example of the sum-product 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 sum-product 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)-
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. 29-Oct. 1, 1997, pp. 666-680.
-
F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product 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 model-based signal processing,” Proc. IEEE, vol. 95, no. 6, pp. 1295–1322, Jun. 2007.
-
H. Wymeersch, Iterative Receiver Design. Cambridge, UK: Cambridge University Press, 2007.
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C. M. Bishop, Pattern Recognition and Machine Learning, 8th ed., ser. Information Science and Statistics. New York, USA: Springer Science+Business Media, 2009.
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