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ANN Models

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.