{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture11 notes

# lecture11 notes - Lecture 11 Optimistic VC inequality...

This preview shows pages 1–2. Sign up to view the full content.

Lecture 11 Optimistic VC inequality. 18.465 Last time we proved the Pessimistic VC inequality: V 1 2 en 2 nt n t 4 n i =1 I ( X i C ) P ( C ) e 8 P sup , V C which can be rewritten with 8 2 en log 4 + V log + u t = V n as 1 n n i =1 8 2 en I ( X i C ) P ( C ) log 4 + V log 1 e u P + u sup . V n C V log n n Hence, the rate is . In this lecture we will prove Optimistic VC inequality, which will improve on this rate when P ( C ) is small. As before, we have pairs ( X i , Y i ), Y i = ± 1. These examples are labeled according to some unknown C 0 such that Y = 1 if X = C 0 and Y = 0 if X / C 0 . Let C = { C : C X} , a set of classifiers. C makes a mistake if X C \ C 0 C 0 \ C = C C 0 . Similarly to last lecture, we can derive bounds on n 1 I ( X i C C 0 ) P ( C C 0 ) sup C , n i =1 where ( ) is the generalization error. P C C 0 Let C = { C C 0 : C C} . One can prove that V C ( C ) V C ( C ) and n ( C , X 1 , . . . , X n ) ≤ � n ( C, X 1 , . . . , X n ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}