# Does “more points” necessarily imply “smoother boundary”?

So in the context of Naive Bayes I encountered a postulate that the more "nearest neighbours" one includes (i.e. the larger the $k$ in $k$-NN), the smoother the boundaries of classes become.

Is this true in general? That the more points, the "smoother" the boundary?

Also, is this concept of smoothness related to some differentiability properties in any way? What's the smoothness used for?

• It is true in general. If you use too few points, you'll have a tendency to overfit. Too many points, and you could underfit. – Adrian Keister Aug 28 '18 at 16:37