#bayes-optimal

Question 1: Single choice

In a multiclass problem, $l(y, y')$ is the penalty for predicting $y'$ when the true class is $y$ , and the model provides $p(y \mid x)$ . Which rule gives the prediction with the smallest expected penalty?

$\hat y = \operatorname*{arg\,min}_{y'} \sum_y l(y, y')\,p(y \mid x)$ 1
$\hat y = \operatorname*{arg\,max}_{y} p(y \mid x)$ 2
$\hat y = \operatorname*{arg\,min}_{y'} \sum_y l(y, y')$ 3
$\hat y = \operatorname*{arg\,max}_{y'} \sum_y l(y, y')\,p(y \mid x)$ 4

Timed test