The sum-product algorithm. (Loopy) Belief Propagation (message passing) for factor graphs

## Project description

`sumproduct <https://pypi.python.org/pypi/sumproduct>`__
========================================================

An implementation of Belief Propagation for factor graphs, also known as
the sum-product algorithm
(`Reference <http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.HomePage>`__).

::

pip install sumproduct

.. figure:: http://f.cl.ly/items/2P021j2y3A2Q191F451h/unnamed0.png
:alt: Simple factor graph

Simple factor graph
The factor graph used in ``test.py`` (image made with
`yEd <http://www.yworks.com/en/products_yed_applicationfeatures.html>`__).

Basic Usage
-----------

Create a factor graph
~~~~~~~~~~~~~~~~~~~~~

::

from sumproduct import Variable, Factor, FactorGraph
import numpy as np

g = FactorGraph(silent=True) # init the graph without message printouts
x1 = Variable('x1', 2) # init a variable with 2 states
x2 = Variable('x2', 3) # init a variable with 3 states
f12 = Factor('f12', np.array([
[0.8,0.2],
[0.2,0.8],
[0.5,0.5]
])) # create a factor, node potential for p(x1 | x2)
# connect the parents to their children
g.append('f12', x2) # order must be the same as dimensions in factor potential!
g.append('f12', x1) # note: f12 potential's shape is (3,2), i.e. (x2,x1)

Run Inference
~~~~~~~~~~~~~

sum-product algorithm
^^^^^^^^^^^^^^^^^^^^^

::

>>> g.compute_marginals()
>>> g.nodes['x1'].marginal()
array([ 0.5, 0.5])

Brute force marginalization and conditioning
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The sum-product algorithm can only compute exact marginals for acyclic
graphs. Check against the brute force method (at great computational
expense) if you have a loopy graph.

::

>>> g.brute_force()
>>> g.nodes['x1'].bfmarginal
array([ 0.5, 0.5])

Condition on Observations
^^^^^^^^^^^^^^^^^^^^^^^^^

::

>>> g.observe('x2', 2) # observe state 1 (middle of above f12 potential)
>>> g.compute_marginals(max_iter=500, tolerance=1e-6)
>>> g.nodes['x1'].marginal()
array([ 0.2, 0.8])
>>> g.brute_force()
>>> g.nodes['x1'].bfmarginal
array([ 0.2, 0.8])

^^^^^^^^^^^^^^^^^^^^^^

``sumproduct`` implements a parallel message passing schedule: Message
passing alternates between Factors and Variables sending messages to all
their neighbors until the convergence of marginals.

Check ``test.py`` for a detailed example.

Implementation Details
----------------------

See block comments in the code's methods for details, but the
implementation strategy comes from Chapter 5 of `David Barber's
book <http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.HomePage>`__.

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:target: https://travis-ci.org/ilyakava/sumproduct
:target: https://pypi.python.org/pypi/sumproduct/

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