LFD Book Forum  

Go Back   LFD Book Forum > Book Feedback - Learning From Data > Chapter 1 - The Learning Problem

Thread Tools Display Modes
Prev Previous Post   Next Post Next
Old 02-07-2014, 07:07 AM
tatung2112 tatung2112 is offline
Junior Member
Join Date: Feb 2014
Posts: 4
Default 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,
Reply With Quote

Thread Tools
Display Modes

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 Jump

All times are GMT -7. The time now is 08:18 AM.

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.