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Notes

Melon Book 01

∑fEote(Ma∣X,f)=∑f∑h∑x∈X−Xp(x)II(h(x)≠f(x))p(h∣X,Ma)=∑x∈X−Xp(x)∑h(h∣X,Ma)∑fII(h(x)≠f(x))\displaystyle{ \begin{aligned}\sum _{ f } E _{ ot e } \left( \mathcal{ M } _{ a } \mid X , f \right) & = \sum _{ f } \sum _{ h } \sum _{ x \in X - \mathcal{ X } } p \left( x \right) \text{II} \left( h \left( x \right) \ne f \left( x \right) \right) p \left( h \mid X , \mathcal{ M } _{ a } \right) \\ & = \sum _{ x \in X - \mathcal{ X } } p \left( x \right) \sum _{ h } \left( h \mid X , \mathcal{ M } _{ a } \right) \sum _{ f } \text{II} \left( h \left( x \right) \ne f \left( x \right) \right)\end{aligned} }