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.

  • $\begingroup$ most common methods are Fourier analysis, Taylor expansion...not aware of a neural network method $\endgroup$ – Andrew Allen Aug 31 '18 at 22:59
  • $\begingroup$ @AndrewAllen Neural network is arguably the most common methods for complicated "curve fitting" problems in recent years. This is an interesting question, and I am a bit surprised it has not been asked before. $\endgroup$ – Cave Johnson Aug 31 '18 at 23:01
  • $\begingroup$ Would ANN's pose any advantage over the aforementioned techniques? $\endgroup$ – Shrey Joshi Aug 31 '18 at 23:46
  • $\begingroup$ It might be difficult to find results which prove the NN techniques perform better, however practically NN's likely outperform classical techniques for large problems where one is looking for an approximate best fit (as opposed to "the" best fit). $\endgroup$ – asd Sep 2 '18 at 3:10

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).


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