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My question is about the 1-nearest neighbor classifier and is about a statement made in the excellent book The Elements of Statistical Learning, by Hastie, Tibshirani and Friedman. The statement is

"For k nearest neighbours the model complexity is controlled by k." "Also as model complexity is increased low bias and high variance"

Now in KNN , if we have a smaller k, we have low bias and high variance.So does that mean a smaller k is a more complex model ?

This seems kind of counter-intuitive as I just chose on basis of 1 point. How is this model more complex?

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  • $\begingroup$ Do those two statements appear near each other? They're both generally accurate, but sometimes they clash with each other. Also, why does it matter? $\endgroup$ – ChootsMagoots Mar 9 '18 at 18:50
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    $\begingroup$ I think it is right, 1NN is the most complex model as it will have the most number of effective parameters = N/k = N and the most convoluted boundaries $\endgroup$ – sww Mar 10 '18 at 5:41
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I think it is right, 1NN is the most complex model as it will have the most number of effective parameters = N/k = N and the most convoluted boundaries

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