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Cake day: October 27th, 2023

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  • The issue here is that you want to extrapolate values outside of the training set (for x>60). You can even get to 0 error, R2=1 on the training data, but it would be meaningless, because you are going to predict outside of this range. If you don’t have data for the range that interests you the best thing you could do is to rely on domain knowledge.

    For example, if you have reason to believe that the function is going to approach an asymptote, you can exploit this knowledge by limiting the class of fitting functions to e.g. parametric sigmoids.

    Or if you know that the process you are modeling has a specific functional type, like logarithmic or squate root, then limit the function space accordingly.

    If you have any other kind of knowledge about your function, it could be used as a prior distribution in a bayesian approach, like bayesian regression or gaussian process

    Bottom line is, there is no magic button “make it work” i ml/statistical modeling, you have to embed your domain knowledge in. The modeling process is not a blind one.