Are there any notable advantages to using Artificial Neural Networks for curve fitting instead of polynomial regression or other techniques?
I'm thinking of doing a project on curve fitting in n dimensions with neural networks and want to see why they might be better.
Polynomial regression is just usually the wrong Bayesian prior. You need functions with highly "non-local" effects which require high-degree polynomials, but polynomial regression gives zero prior probabilities to high-degree polynomials. As it turns out, neural networks happen to provide a reasonably good prior (perhaps that's why our brains work that way -- if they even do).