My Science Fair Project is on Curve fitting with neural nets as an alternative to polynomials. I know this is a widely done procedure in datascience but I wanted to do my own research on it. Currently the biggest problem is training time, and to solve that I had an idea. What if I I trained an ANN to predict the degree of the polynomial that best fits the model then use standard polynomial regression to curve fit. This would make the training only happen once so I could train for as long as I wanted, and thus it would increase speed by a lot. What are your thought in this? Has anyone done this before? Is it plausible?
Interesting idea :)
The things I would consider:
Should it be classification or regression? If you define it as classification, you should select the number of classes, hence the maximum and minimum polynomial degree (e.g. 1,2,3,4,5,6,7,8,9 and 10 could be polynomial degrees which you recognize).
If you select regression, you don't need to define the maximum number of classes, but the output layers could be trickier to define.
How do you define your samples? I guess that it's easy to generate samples (select some polynomial with degree $n$, sample points from it and then all those points define one sample for class (or regression value)
It would be interesting to create the image out of the sample (plot of points) and then maybe use a convolutional network to learn the classification (or regression).
Also, consider how dataset big should be. It's hard to say, you will have to test it and see how big it should be.
For classification probably cross entropy and for regression probably mean squared error.
Let me know the results.