Unformatted text preview: Optimistic VC inequality, which will improve on
� this rate when P (C ) is small. As before, we have pairs (Xi , Yi ), Yi = ±1. These examples are labeled according to some unknown C0 such that Y = 1 if X = C0 and Y = 0 if X ∈ C0 . /
Let C = {C : C ⊆ X }, a set of classiﬁers. C makes a mistake if X ∈ C \ C0 ∪ C0 \ C = C �C0 .
Similarly to last lecture, we can derive bounds on
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n
�1 �
�
�
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sup �
I (Xi ∈ C �C0 ) − P (C �C0 )� ,
�n
�
C
i=1
where P (C �C0 ) is the generalization error.
Let C � = {C �C0 :...
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This note was uploaded on 01/23/2014 for the course MATH 18.465 taught by Professor Panchenko during the Spring '07 term at MIT.
 Spring '07
 Panchenko
 Statistics

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