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Old 10-21-2014, 11:20 PM
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yaser yaser is offline
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Location: Pasadena, California, USA
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Default Re: Exercise 1.13 noisy targets

Originally Posted by mahaitao View Post
Exercise 1.13(a): what is the probability of error that h makes in approximating y if we use a noisy version of f. That means we want to compute Pr(h(x)~=y), and I consider two cases:
(1) h(x)=f(x) and f(x) != y; [(1-\mu)*\(1-\lambda)]
(2) h(x)!=f(x) and f(x) = y. [\mu*\lambda]
I am not sure the solution is right. My questions are follows:
(i) Does "h makes an error with \mu in approximating a deterministic target function f" mean Pr(h(x) != f(x)) = \mu?
(ii) Does the probability of Pr(h(x)~=y)=Pr(1)+Pr(2)?

Exercise 1.13(b) : I am not clear what does "performance of h be independent of \mu" mean? Should I consider Pr(h(x)~=y)?

Answering your questions (i) and (ii): Yes and yes.

In Exercise 1.13(b): Independent of \mu means that changing the value of \mu does not affect how well h({\bf x}) predicts y.
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