<a name="p-138350-i-mean-it-is-always-said-that-complex-model-high-variance-and-simple-model-high-bias-i-wonder-what-if-we-fit-a-linear-model-by-complex-polynomial-regression-eg-y_i-wx_i-epslion-if-we-fit-this-true-linear-model-by-a-high-order-polynomial-regression-do-we-also-have-a-higher-bias-than-linear-regression-since-bias-is-defined-as-the-expectation-of-generation-error-besides-regards-to-parameter-space-polynomial-regression-indeed-contains-linear-regression-is-there-a-contradiction-or-my-misunderstanding-thanks-like-in-the-picture-will-the-rightmost-model-has-higher-bias-than-the-second-one-since-bias-is-the-expectation-of-generalisation-error-on-not-only-training-set-1" class="anchor" href="#p-138350-i-mean-it-is-always-said-that-complex-model-high-variance-and-simple-model-high-bias-i-wonder-what-if-we-fit-a-linear-model-by-complex-polynomial-regression-eg-y_i-wx_i-epslion-if-we-fit-this-true-linear-model-by-a-high-order-polynomial-regression-do-we-also-have-a-higher-bias-than-linear-regression-since-bias-is-defined-as-the-expectation-of-generation-error-besides-regards-to-parameter-space-polynomial-regression-indeed-contains-linear-regression-is-there-a-contradiction-or-my-misunderstanding-thanks-like-in-the-picture-will-the-rightmost-model-has-higher-bias-than-the-second-one-since-bias-is-the-expectation-of-generalisation-error-on-not-only-training-set-1" aria-label="Heading link"> I mean it is always said that complex model high variance and simple model high bias. I wonder what if we fit a linear model by complex polynomial regression. E.g. y_i = w*x_i + epslion . If we fit this true linear model by a high order polynomial regression. Do we also have a higher bias than linea…

Thanks for the reply. Is says that bias “can relate to the model prediction and can be on any part of the data - training, validation or test set. It just means what kind of error you are seeing in your predictions w.r.t to the actual data.”. And " for some simple datasets with linear relationships…

If viewing this as hypothesis space. Bias is defined to be the sum of estimation bias and approximation error. Where approximation error is just the same for linear and polynomial model. But will the approximation bias increases as the order of polynomial increases?

Will complex model increase bias

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paulinpaloalto January 2, 2022, 6:46pm 2

Here’s a recent post that goes into quite a bit of detail on the meaning of bias and variance.

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Will complex model increase bias

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