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Not rubbish at all!
Probabilistic networks have many advantages over the neural networks:
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Probabilistic networks allow you to input information at any node, not just
the input nodes. For example, if information comes concerning an intermediate
node, it is used in a diagnostic way to draw conclusions about the "parents"
of this node and in a causal way in order to draw conclusions about the
"children" of this node. Suppose that somebody were to tell you that the
erosion of a burned forest is very high. Immediately you could feed this
information into the network and it could be used to update the probability
with which this site is predicted to be in some risk of desertification state,
but also to update the confidence you have in the sources of your data concerning
the soil depth of this site, its slope, etc.
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Probabilistic networks allow you to have input variables for factors for
which data may not be available. For example, in the network we constructed
earlier, the factor "animal grazing" may be modelled by the number of animals
in the region, the distance of the nearest village or the nearest water
hole, etc. In many cases this information may not be available. Then all
you have to do is give all states of this variable equal probability
i.e. 0.33 in the state "heavily grazed", 0.33 in the state "moderately grazed"
and 0.33 in the state "slightly grazed". This is equivalent to ignoring this
factor when you run the network for this site. However, if you were
using neural networks, you would have to have two separate networks, one
for the case you had information on animal grazing and one for the case you
had not. These networks would have different architectures (different
number of input nodes) and would have to be trained separately. The
same would apply if you wanted to cover the situation that information on
soil depth was missing and so on. In other words neural networks do
not allow you to include nodes which sometimes are used and sometimes are
not used.
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Neural networks are linear classifiers. Imagine a multidimensional space
where we measure one input variable along each axis. A burned forest according
to the value of its variables would be represented by a point in this space.
Suppose that we wanted to draw surfaces which would divide this space into
regions occupied by points representing forests that run low risk of
desertification, regions occupied by points representing forests that run
moderate risk of desertification, and so on. A neural network draws these
surfaces by approximating them with planes. The probabilistic network draws
these surfaces so that the system that classifies a burned forest into one
of these classes makes the minimum error.
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When the neural network assigns a burned forest to a risk class, it does
not tell you how confident you should be about this decision. On the contrary,
the probabilistic network tells you with what probability the forest
belongs to each one of its possible classes. It will be up to you then to
make the most of this information. For example, the neural network may tell
you: "This burned forest belongs to class `high risk' of desertification."
The probabilistic network will tell you something like: "This burned forest
belongs to class `high risk' of desertification with probability 50%, to
class `moderate risk' with probability 40% and to class `no risk' with
probability 10%." It will be your choice then if you like to "harden" this
decision i.e. to take the most probable class and use it, ignoring the
corresponding probability.
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