xiwenc1 / sumproduct

Sum product algorithm - Belief propagation (message passing) for factor graphs

sumproduct

An implementation of Belief Propagation for factor graphs, also known as the sum-product algorithm (Reference).

pip install sumproduct

The factor graph used in test.py (image made with yEd).

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.add(f12)
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])

Additional Information

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.