Row 32176

Row ID: 32176 | Dataset Entry | Axioma AXP Content Repository

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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.

For 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.

FieldValue
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. For example, consider the…
label r/machinelearning
dataType comment
communityName r/MachineLearning
datetime 2024-05-21
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{
  "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",
  "username_encoded": "Z0FBQUFBQm5Lak1ITjhBUmZZaU9sRnI0MnRvWC1JeXNUNzBHOWhlcjZHWE5kOEhhS0dyVERMUWZiUFBGM1pZSFNJbjJWV1FweFMyNFg5TkFaeG9tWlZxRVJKS1BHRlZmeHc9PQ==",
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}
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