Bayes classifier
Properties

Define the variables: Risk R (h) {\displaystyle R(h)}, Bayes risk R ∗ {\displaystyle R^{*}}, all possible classes to which the points can be classified Y = { 0, 1 } {\displaystyle Y=\{0,1\}}. Let the posterior probability of a point belonging to class 1 be η (x) = P r (Y = 1 | X = x) {\displaystyle \eta (x)=Pr(Y=1|X=x)}. Define the classifier h ∗ {\displaystyle {\mathcal {h}}^{*}} as h ∗ (x) = { 1 if η (x) ⩾ 0.5, 0 otherwise. {\displaystyle {\mathcal {h}}^{*}(x)={\begin{cases}1&{\text{if }}\eta (x)\geqslant 0.5,\\0&{\text{otherwise.}}\end{cases}}}
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