11_StatisticalLearningTheory - 10/16/2009 Example: Smart...

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10/16/2009 1 Statistical Learning Theory Example: Smart Investing Task: Pick stock analyst based on past performance. Experiment: Have analyst predict “next day up/down” for 10 days. Pick analyst that makes the fewest errors. Situation 1: 1 stock analyst {A1}, A1 makes 5 errors Situation 2 Situation 2: 3 stock analysts {A1,B1,B2}, B2 best with 1 error Situation 3: 1003 stock analysts {A1,B1,B2,C1,…,C1000}, C543 best with 0 errors Which analysts are you most confident in: A1, B2, or C543? Outline Questions in Statistical Learning Theory: How good is the learned rule after n examples? How many examples do I need before the learned rule is accurate? What can be learned and what cannot? Is there a universally best learning algorithm? In particular, we will address: What is the true error of h if we only know the training error of h ? Finite hypothesis spaces and zero training error (Finite hypothesis spaces and non zero training error) Game: Randomized 20 Questions Game: 20 Questions I think of object f For i = 1 to 20 You get to ask 20 yes/no questions about f and I have to answer truthfully You make a guess h You win, if f=h Game: Randomized 20 Questions I pick function f H , where f : X { 1,+1} For i = 1 to 20 World delivers instances x X with probability P(x) and I have to tell you f(x) You form hypothesis h H trying to guess my f H You win if f(x)=h(x) with probability at least 1 ‐ε for x drawn according to P(x).
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11_StatisticalLearningTheory - 10/16/2009 Example: Smart...

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