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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 doesn’t 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 What’s 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) Sauer’s 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 What’s the Best Separating Hyperplane? + + + + + + 7 What’s the Best Separating Hyperplane? + + + + + + 8 What’s the Best Separating Hyperplane? + + + + + + 9 What’s the Best Separating Hyperplane?...
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This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Levinson,S

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