Bayes Classifier is Risk Minimizer

Last updated Nov 1, 2022

Let $X, Y, n$ be a Classification Problem. Then the Bayes Classifier minimizes Risk. It is the unique minimizer up to modifications on $\mathbb{P}$-Null Sets of $\mathcal{D}$ and subsets of $E = {x \in \mathcal{D} : \mathbb{P}(Y=y|X) = \frac{1}{n} \forall y \in [n]}$.