Random Classifier

Last updated Nov 1, 2022

Let $(X, Y, n)$ be a Classification Problem. Let $f: \mathcal{D} \to \mathcal{P}^{n}$. Then a Random Classifier is a Random Variable $F$ on $[n]$ s.t. $\forall i \in [n]$ $$\mathbb{P}(F=i | X=x) = f(x).$$ $\mathcal{P}^{n} = {t \in [0,1]^{n} : \sum\limits_{i=1}^{n} t_{i} = 1}$ is the Set of Probability Mass Functions on $n$ elements.