ANN models transform inputs into outputs in the following way:
First, a number of weighted sums of all the inputs are formed. Each
weighted sum is then transformed by a sigmoid function to produce
a set of nodal values. These values are considered the outputs of
the first "hidden layer" nodes. These outputs are then
transformed into another set of nodal values in the same way. This
may be continued any number of times.
Finally, the last hidden layer passes its values as a weighted
sum to an "output" node, which forms the final result
of the model. The ANN model is made to work by iteratively adjusting
the values of the weights in the model until a sufficiently accurate
prediction is made for a test set of input and output values. Weights
are determined by an optimization scheme such as "back-propagation."
The ANN model has several advantages. There is considerable freedom
in selecting model structure. The number of hidden layers and nodes
in each hidden layer is simply increased until no further improvement
can be obtained. ANN's can reproduce nonlinear behavior. An important
advantage is that they are fairly easy to apply to high-dimensionality
systems, such as graphical pattern recognition problems.
A number of disadvantages have been noted with ANN's. It is difficult
to determine which weights are important to the model; thus the
model may be overspecified, leading to overfitting or "memorization"
of test data. The values obtained for the weights do not directly
yield information on the behavior of the model, particularly on
its sensitivity or causal relationships. ANN models do not lend
themselves to statistical analysis; confidence intervals on forecasts
are not easily computed. ANNs require very large amounts of computational
time to fit a single set of data; it is not unusual to allow fitting
procedures to run for many days on workstation computers. Perhaps
most importantly, ANNs are difficult to communicate to others. Thus
investigators tend to develop ANNs only for use by themselves, and
not to disseminate the models to a wider community.