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christophM / interpretable-ml-book

Book about interpretable machine learning
https://christophm.github.io/interpretable-ml-book/
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Found introduction on splines in 5.3. confusing #312

Closed brshallo closed 2 years ago

brshallo commented 2 years ago

(Caveat that this may be my own misunderstanding or just me having trouble connecting related explanations between what's in IML with the way the topic is introduced in ISLR.)

I found your introduction on splines in 5.3 a bit confusing to my general understanding of splines, specifically:

Splines are functions that can be combined in order to approximate arbitrary functions. A bit like stacking Lego bricks to build something more complex...

My understanding is that this description applies more to basis functions which are ultimately used to build splines (typically). So it's more that basis functions are stacked to build smoothed splines -- and that the intuition for splines is more about fitting non-linear models that can have different characteristics in different regions (which is why they are usually introduced after polynomial piecewise regression).

I don't know if there may be another way of introducing splines here in a way that gets across the typical intuition provided on splines (e.g. regarding knots) but that also sets-up the basis functions used to build them and that therefore segways nicely with GAMs...

christophM commented 2 years ago

How did I miss this ... You are absolutely right, I muddled together the splines and spline basis functions. Thanks for pointing it out, I tried to make the distinctions clearer.