Exercise 1.11
Thank you Prof. Yaser. Your book is really easy to follow. I have just started it for a week and I am trying to finish every exercises in the book.
About exercise 1.11, I don't know where to check the answer so I post it here. Could you please tell me whether my answers are right or wrong? Is there any place that I can check my answer on exercise by myself? Ex 1.11: Dataset D of 25 training examples. X = R, Y = {1, +1} H = {h1, h2} where h1 = +1, h2 = 1 Learning algorithms: S  choose the hypothesis that agrees the most with D C  choose the hypothesis deliberately P[f(x) = +1] = p (a) Can S produce a hypothesis that is guaranteed to perform better than random on any point outside D? Answer: No In case that all examples in D have yn = +1 (b) Is it possible that the hypothesis that C produces turns out to be better than the hypothesis that S produces? Answer: Yes (c) If p = 0.9, what is the probability that S will produce a better hypothesis than C? Answer: P[P(Sy = f) > P(Cy = f)] where Sy is the output hypothesis of S, Cy is the output hypothesis of C + Since yn = +1, Sy = +1. Moreover, P[f(x) = +1] = 0.9 > P(Sy = f) = 0.9 + We have, P(Cy = +1) = 0.5, P(Cy = 1) = 0.5, P[f(x) = +1] = 0.9, P[f(x) = 1] = 0.1 > P[Cy = f] = 0.5*0.9 + 0.5*0.1 = 0.5 Since 0.9 > 0.5, P[P(Sy = f) > P(Cy = f)] = 1 (d) Is there any value of p for which it is more likely than not that C will produce a better hypothesis than S? Answer: p < 0.5 I am not sure that my answer of (a) and for (c) is not conflict. Thank You and Best Regards, 
Re: Exercise 1.11
Quote:

Re: Exercise 1.11
Prof. Yaser, thank you very much for your replying. I will keep studying. Thank you!

Re: Exercise 1.11
Hi,
according to the first post, I can't understand why the answer to the question (d) is p < 0.5. Intuitively my answer is that there are no values of p that make probabilistically C better than S. That's why S try to minimize the error on the training data which should reflect the true distribution. In this case, C do better than S only if (the majority of the examples are +1 GIVEN p < 0.5) OR (the majority of the examples are 1 GIVEN p > 0.5). However both the cases are less probable than the ones for which S works better. As a results, there are no value for p to reverse the situation. Am I right ? 
Re: Exercise 1.11
Quote:
https://scontentfra31.xx.fbcdn.net...fa&oe=572933FD 
Re: Exercise 1.11
"(a) Can S produce a hypothesis that is guaranteed to perform better than random on any point outside D?"
Can anyone give me some tips on this part of the exercise: (1) Should we calculate it to be sure that S guarantees/(does't guarantee) to beat random result? If so, any tip is appreciated to deal with this deterministic task. (3) Does "any point" in this context mean "every point" or "some point"? 
Re: Exercise 1.11
Quote:
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] = = 0.9999998379165839813935344 It is quite different from tatung2112's explanation for c. Could you comment further? Thanks! 
Re: Exercise 1.11
Quote:
Now, I am even more confused. 
Re: Exercise 1.11
Quote:

All times are GMT 7. The time now is 03:08 PM. 
Powered by vBulletin® Version 3.8.3
Copyright ©2000  2021, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. AbuMostafa, Malik MagdonIsmail, and HsuanTien Lin, and participants in the Learning From Data MOOC by Yaser S. AbuMostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.