#amplitude

Question 1: Single choice

easyAI-checkedNearest Neighbors & Kernel Methods

In the RBF kernel $k(x, x') = a^2 \exp\left(-\frac{\lVert x - x' \rVert^2}{2\ell^2}\right)$ you raise the amplitude $a^2$ from 1 to 4 and keep $\ell$ fixed. What happens to the prior sample functions?

Their vertical spread doubles; how fast they wiggle is unchanged1
Their vertical spread grows fourfold, as the variance grew fourfold2
They wiggle twice as fast, because a larger amplitude acts like a shorter length-scale3
They get smoother, because a larger covariance links neighbouring values more strongly4

Timed test