 LFD Book Forum Exercise 1.13 noisy targets
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 ckong41 Junior Member Join Date: Apr 2021 Posts: 2 Re: Exercise 1.13 noisy targets

Quote:
 Originally Posted by prithagupta.nsit SO final Probability of error that h makes in approximating y would be: 1+2*lamda*mu -mu -lamda.
Anyone know how this user arrived at this step?
#12 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 610 Re: Exercise 1.13 noisy targets

Quote:
 Originally Posted by ckong41 Anyone know how this user arrived at this step?
I think it can be derived by calculating (1-mu) * (1-lambda)+mu * lambda . Hope this helps.
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#13
 anon4 Junior Member Join Date: May 2021 Posts: 2 Re: Exercise 1.13 noisy targets

I don't understand why the case y != f(x) and h(x) != f(x) doesn't count toward the probability that y != h(x). We have four cases:
(1) y = f(x) and h(x) = f(x) imply y = h(x);
(2) y != f(x) and h(x) = f(x) imply y != h(x);
(3) y = f(x) and h(x) != f(x) imply y != h(x);
(4) y != f(x) and h(x) != f(x) imply neither y = h(x) or y != h(x).
For instance if at x = 0 we had y = 1, h(0) = 2 and f(0) = 3, then we are in case (4) and y != h(x). But if at x = 1 we had y = 4, h(1) = 4 and f(1) = 5, then we are in case (4) and y = h(x). What am I missing?
#14 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 610 Re: Exercise 1.13 noisy targets

Quote:
 Originally Posted by anon4 I don't understand why the case y != f(x) and h(x) != f(x) doesn't count toward the probability that y != h(x). We have four cases: (1) y = f(x) and h(x) = f(x) imply y = h(x); (2) y != f(x) and h(x) = f(x) imply y != h(x); (3) y = f(x) and h(x) != f(x) imply y != h(x); (4) y != f(x) and h(x) != f(x) imply neither y = h(x) or y != h(x). For instance if at x = 0 we had y = 1, h(0) = 2 and f(0) = 3, then we are in case (4) and y != h(x). But if at x = 1 we had y = 4, h(1) = 4 and f(1) = 5, then we are in case (4) and y = h(x). What am I missing?
This case is about binary classification, where all the outputs are +/- 1. So your cae (4) actually implies that y = h(x). Hope this helps.
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#15
 anon4 Junior Member Join Date: May 2021 Posts: 2 Re: Exercise 1.13 noisy targets

Yes, it makes much more sense now hahaha  Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
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