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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 Computational Learning Theory How Much Data is Enough? • Training set is evidence for which h H is – Correct: [Simple, Proper, Realizable??] learning – Best: Agnostic learning • Remember: training set = labeled independent samples from an underlying population • Suppose we perform well on the training set • How well will perform on the underlying population? • This is the test accuracy or utility of a concept (not how well it classifies the training set) 2 What Makes a Learning Problem Hard? • How do we measure “hard”? • Computation time? • Space complexity? • What is the valuable resource? • Training examples • Hard learning problems require more training examples • Hardest learning problems require the entire example space to be labeled 3 [Simple] Learning • PAC formulation • Probably Approximately Correct • Example space X sampled with a fixed but unknown distribution D • Some target concept h* H is used to label an iid (according to D ) sample S of N examples • Finite H • Algorithm: return any h H that agrees with all N training examples S  S  = N • Choose N sufficiently large that with high confidence (1 ) h has accuracy of at least 1 0 < , << 1 H N ln 1 ln 1 4 Simple Learning (simple derivation) • What is the probability that a bad hypothesis looks good?...
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 Fall '08
 Levinson,S
 Machine Learning, ln H, ln ln, VC Dimensions

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