Data:
{
"text": "It depends on what you mean by \"extrapolate\". What I learned is that a polynomial basis has a \"natural domain\" of approximation. So the regular power basis has the complex unit circle as its \"natural domain\". That's exactly Fourier analysis. The Bernstein basis has the interval \\[0, 1\\] as its \"natural domain\". So as long as your input features are properly normalized to the natural domain, there is no real problem with high degree polynomials if you use a good basis. \n\nFor example, consider the Bernstein basis. If the vast majority of your data is in \\[0, 0.5\\], or even if all of your data is in \\[0, 0.5\\], extrapolation in \\[0.5, 1\\] is not really a problem. Outside of the \"natural domain\", I think we should say that our basis is \"undefined\", even if we are used to defining polynomials over the entire real line.",
"label": "r/machinelearning",
"dataType": "comment",
"communityName": "r/MachineLearning",
"datetime": "2024-05-21",
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}