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Unformatted text preview: Announcements Final 78:15 PM, Wed. 12/15 here Q/A session 11noon Mon. 12/13 2405SC Projects (for 4 credits) due Tue. 12/7 Code Sample I/O (if it doesnt work, say so) Paper discussing What you did & why What you learned How you would do it differently given 1 VC Dimension of a Concept Class Can be challenging to prove Can be nonintuitive Signum(sin( x)) on the real line Convex polygons in the plane 2 Learnability Often the hypothesis space (or concept class) is syntactically parameterized nConjuncts, kDNF, k CNF, m of n, MLP w/ k units, The concept class is PAC learnable if there exists an algorithm whose running time grows no faster than polynomially in the natural complexity parameters: 1/ , 1/ , others Clearly, polynomiallybounded growth in the minimum number of training examples is a necessary condition. 3 Suppose All h H are very low accuracy, say < 0.1% correct VC(H) is 100 Training set S contains 80 labeled examples Whats the probability that an arbitrary h gets the first training example right? What is the best some h H can possibly do on all 80 elements of S? Will this h work well in general? 4 log(labelings) vs. S S labelings(S) 1 100 10,000 1,000,000 5 10 20 15 All Labelings (exponential growth) Labelings Possible by H (polynomial growth after VC(H) Sauers Lemma) VC(H) 5 Back to Perceptrons (linear threshold units, linear discriminators) If there is one perceptron, there are many Are some better? Is one best? Can we tell? Can we find it? 6 Whats the Best Separating Hyperplane? + + + + + + 7 Whats the Best Separating Hyperplane? + + + + + + 8 Whats the Best Separating Hyperplane? + + + + + + 9 Whats the Best Separating Hyperplane?...
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 Fall '08
 Levinson,S

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