Thread: Exercise 1.11
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Old 05-29-2016, 09:44 AM
henry2015 henry2015 is offline
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Default Re: Exercise 1.11

Quote:
Originally Posted by yaser View Post
Your answers to (a) and (c) are both correct. They are not in conflict since (a) is asking a deterministic question while (c) is asking a probabilistic question.
For part c, I thought:

Given p = 0.9, h1 is a better hypothesis than h2.

Hence, the probability that S produces a better hypothesis than C is the probability that S picks h1 essentially as C will pick the other hypothesis that S doesn't pick.

In other words, P[S produces a better hypothesis than C] = P[S picks h1 based on the 25 training examples].

S will pick h1 if 13 out of 25 training examples give +1, so we will have:
P[S picks h1]
= P[13 or more out of 25 training examples give +1]
= \sum_{k = 13}^{25}\binom{25}{k}(.9)^{k}(.1)^{25-k}
= 0.9999998379165839813935344

It is quite different from tatung2112's explanation for c.

Could you comment further?

Thanks!

Last edited by henry2015; 05-29-2016 at 09:48 AM. Reason: fixing latex syntax
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