Problem II

Assume we use classifiers from a countably finite model class $F$ of $1000000$ classifiers. On a

dataset of $20$ i$.$i$.$d$.$ samples, we obtain an empirical risk $($i$.$e$.,$ training error$)$ of $0\mathrm{.}35.$

Would you recommend using this classifier or not? Assume we want to be certain with probability at least

$0\mathrm{.}99.$ Please answer "Yes" or $"$No$",$ and clearly explain why.

Assume we use classifiers from a countably finite model class $F$ of $2000000$ classifiers. On a

dataset of $1000$ i$.$i$.$d$.$ samples, we obtain an empirical risk $($i$.$e$.,$ training error$)$ of $0\mathrm{.}1.$

Would you recommend using this classifier or not? Assume we want to be certain with probability at least

$0\mathrm{.}99.$ Please answer "Yes" or $"$No$",$ and clearly explain why.

On another dataset with $p100$ features, assume we run $3$ classification algorithms and obtain

the following empirical risks $($i$.$e$.,$ training errors$).$ We also include the VC dimension of the $3$ algorithms.

Which algorithm should we prefer? Write $"$A$1"$ or $"$A$2"$ or $"$A$3",$ and clearly explain your answer.