

![0_image_0.png](0_image_0.png)

Se ondly, the lo al probability tables are of a form that is diÆ
ult for the bound propagation algorithm. That is, a lot of probabilities are lose to zero and one.

This pi ture is what we generally see. There are some parts in the network that are hard to ompute (not ne essarily impossible) whi h usually have a more dense stru ture and a larger (lo al) state spa e. Other parts an be bounded very well. Note that this network ould easily be embedded in a very large network that is intra table for any exa t method.

Even in that ase, the bound propagation algorithm ould be used to nd similar results.

Sin e the method is based on lo al omputations, the existan e of a large surrounding network has almost no in uen e.

## 5.2 A Large Ising Grid

We reated a so alled two-dimensional Ising model, whi h is a re tangular grid with on-

```
ne
  tions between all pairs of nodes that are dire
                             t neighbours. We used a grid of 40 by 40
                                                       

```

binary nodes. The potentials were drawn from a uniform distribution between zero and one.

In ontrast with Bayesian belief networks (Neal, 1992) the probability distribution over the un lamped Ising grid is not automati ally normalized, but this has no onsequen es for the algorithm.

