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lecture11-annotated - Machine Learning 10-701/15-781 Fall...

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1 © Eric Xing @ CMU, 2006-2008 1 Machine Learning Machine Learning 10 10- 701/15 701/15- 781, Fall 2008 781, Fall 2008 Computational Learning Theory II Computational Learning Theory II Eric Xing Eric Xing Lecture 11, October 13, 2008 Reading: Chap. 7 T.M book, and outline material © Eric Xing @ CMU, 2006-2008 2 Last time: PAC and Agnostic Learning z Finite H, assume target function c H z Suppose we want this to be at most δ . Then m examples suffice: z Finite H, agnostic learning: perhaps c not in H z Î z with probability at least (1- δ ) every h in H satisfies
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2 © Eric Xing @ CMU, 2006-2008 3 What if H is not finite? z Can’t use our result for infinite H z Need some other measure of complexity for H – Vapnik-Chervonenkis (VC) dimension! © Eric Xing @ CMU, 2006-2008 4 What if H is not finite? z Some Informal Derivation z Suppose we have an H that is parameterized by d real numbers. Since we are using a computer to represent real numbers, and IEEE double-precision floating point (double's in C) uses 64 bits to represent a floating point number, this means that our learning algorithm, assuming we're using double-precision floating point, is parameterized by 64d bits z Parameterization
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