#ornstein-uhlenbeck

Question 1: Single choice

mediumAI-checkedNearest Neighbors & Kernel Methods

You draw prior sample functions from a zero-mean GP with the Ornstein–Uhlenbeck (exponential) kernel $k_{\textrm{OU}}(x, x') = \exp\left(-\frac{|x - x'|}{2\ell}\right)$ and from a GP with the RBF kernel with the same $\ell$ . How do the OU samples look different?

They are continuous but jagged, with no derivative anywhere, while RBF samples are very smooth1
They are smoother, because $|x - x'|$ grows more slowly than its square2
They look about the same, because both kernels decay with distance at a rate set by the same $\ell$ 3
They repeat periodically, because the absolute value makes the kernel symmetric4

Timed test