Numerical instabilities in sum-product belief propagation?

[Lars Mescheder]

Hi,
First, thanks for all the hard work you put into making opengm. It's a great library that is easy to use.

However, sometimes, sum-product belief propagation gives me marginals that do not sum to one:

import opengm
import numpy as np

def infer_bp(potv, potf, indv):
    N = potv.shape[0]
    F = potf.shape[0]
   
    gm = opengm.gm([2] * N, 'multiplier')
   
    fids = gm.addFunctions(potv)
    gm.addFactors(fids, np.arange(N))
    fids = gm.addFunctions(potf)
    gm.addFactors(fids, indv)
   
    bp = opengm.inference.BeliefPropagation(gm, 'integrator')
    res = bp.infer()
    print res
   
    margv = bp.marginals(np.arange(N))
    margf = bp.factorMarginals(np.arange(N, N+F))

    return margv, margf

N = 100
F = N - 1
potv = np.zeros((N, 2), dtype=np.float64)
potf = np.zeros((F, 2, 2), dtype=np.float64)
indv = np.zeros((F, 2), dtype=np.int32)

potv[:, :] = np.array([1e2, 1e0])
potf[:, :] = np.array([[1e0, 1e2], [1e0, 1e-2]])
indv[:, 0] = 0
indv[:, 1] = np.arange(1, F+1)

margv, margf = infer_bp(potv, potf, indv)

print margv[:10]

results in

NORMAL
[[  3.64091745e-18   5.80150354e-50]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]
 [  5.40748338e-18   5.40748338e-18]]

Of course, this is an artificial example, but a similar case arises in my research code. Note that for N=10 there are no issues (marginals sum to 1). Any suggestions?