Expert: George Moustris - 2/2/2005

Question
Hello George,
    I have been told that for neural network to show superior accuracy, about million pieces of data will be needed.  I have been advised that quadratic regression analysis will be satisfactory most of the time.  When I have used both methods on a set of several hundred pieces of data, if anything, regression analysis has been a little more accurate.  So, as a beginning user of neural network, I am not understanding what is so great about neural networks.  Do you also think for neural network to be accurate, a lot (~million) pieces of data are needed?

Answer
Hi Glen

Artificial Neural Networks (ANNs) are not only used in data fitting. The have many other uses which make them a rather unique tool (pattern recognition, associative memory, system identification, control, modeling etc.). Nevertheless one of its main uses is function approximation. ANNs don't need "a million data pieces" in order to be accurate. The accuracy of ANNs depends on many factors such as the number of hidden layers, the activation function, the learning algorithm and of course the learning data. It is a well established theorem in ANNs theory that an ANN with just one hidden layer and "sufficient" number of neurons can approximate infinitely close any function (or relation). This is the Kolmogorov Theorem. That's why ANNs are also called Universal Function Approximators. What is not known however, is the exact number of neurons to achieve such a precision.
Anyway, if you read more about ANNs i'm sure you'll see their uniqueness and usefullness.

Best G.