#length-scale

Question 1: Select all that apply

mediumAI-checkedNearest Neighbors & Kernel Methods

You skip hyperparameter learning in GP regression with an RBF kernel and set the length-scale $\ell$ and the noise variance $\sigma^2$ by hand. Which outcomes do you expect? Select all that apply.

A very large $\ell$ gives an over-smooth mean that misses fast variation in the data1
A very small $\ell$ makes the uncertainty grow quickly between and away from the training points2
A large $\sigma^2$ lets the mean pass farther from the data points, treating more variation as noise3
A small $\sigma^2$ makes the mean smoother, because the model then trusts the prior more4
Changing $\ell$ moves the predictive mean but leaves the width of the credible band unchanged5

Timed test