Polynomial Regression — An Alternative For Neural Networks?

A discussion of polynomials and neural networks, which theoretically are both able to approximate continuous functions infinitely closely

Example of polynomial regression performed on a data set, using three different degrees of polynomials. Theoretically, polynomials can achieve infinitely close fits. [image from WikiMedia by Shobha]

To start: this is more a discussion piece than anything else. Although I will attempt to compare polynomials and neural networks, there…