Will complex model increase bias

[donnie1123]

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 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)?

[paulinpaloalto]

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

[donnie1123]

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, linear regression is good enough and it’ll have a low bias and variance". But it did not quite solve my question. Like fitting a polynomial regression on linear relation datasets, will the bias increase as the order of polynomial increases? (Since linear has a 0 bias but polynomial may not necessarily be unbiased). Thanks

[donnie1123]

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?