I tried not to be that guy and already gave some alternatives for regression.
“Polynomial regression” implies to me that the basis functions are polynomials. I‘ll assume you meant “good basis for a simple fit, maybe by least squares”. More local functions like “radial basis functions” can work well. Or use splines or sigmoidal functions, which saturate to a flat line or linear trend. In some applications Fourier or wavelet bases might be appropriate.
Gaussian process regression is a Bayesian treatment of some basis function models, potentially with an infinite number of basis functions. Artificial neural nets usually use local or sigmoidal basis functions, potentially in a more complicated way.
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I tried not to be that guy and already gave some alternatives for regression.
“Polynomial regression” implies to me that the basis functions are polynomials. I‘ll assume you meant “good basis for a simple fit, maybe by least squares”. More local functions like “radial basis functions” can work well. Or use splines or sigmoidal functions, which saturate to a flat line or linear trend. In some applications Fourier or wavelet bases might be appropriate.
Gaussian process regression is a Bayesian treatment of some basis function models, potentially with an infinite number of basis functions. Artificial neural nets usually use local or sigmoidal basis functions, potentially in a more complicated way.