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846Excercise 18.14, page 677

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  • Nima Talebi
    Oct 23, 2008
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      I'm interested to see if my solution is even remotely correct, the question is to derive the error formula given the number of experts/hypotheses (M) and also the error of each hypotheses (e) - assuming all to be the same, and that all are independent of one another...

      I treated this as a probability problem (and unsure if I should have done so), and hence derived a formula which yields the following results...

      M:5, e:0.10, 0.0100
      M:5, e:0.20, 0.0800
      M:5, e:0.40, 0.6400
      M:10, e:0.10, 0.0002
      M:10, e:0.20, 0.0134
      M:10, e:0.40, 0.8602
      M:20, e:0.10, 0.0000
      M:20, e:0.20, 0.0034
      M:20, e:0.40, 7.0448

      The third column is the total error for the network I calculated; it certainly looks wrong from looking at the last value, but I'd like to know how to go about solving this as it's rather intriguing.

      My `formula' in Python form is as follows...

      def fact(k):
        return reduce(lambda i, j : i*j, range(1, k+1))

      for M in 5, 10, 20:
        for e in 0.1, 0.2, 0.4:
          m  = M/2+1
          _m = M-m

          print "M:%d, e:%0.2f, %0.4f"%(M, e, (fact(M) * pow(e, m))/(fact(_m) * fact(m)))
      Thanks to anyone who has a crack at solving this =)


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