 LFD Book Forum *ANSWER* Stuck on #4
 User Name Remember Me? Password
 Register FAQ Calendar Mark Forums Read Thread Tools Display Modes
#1
 mvellon Junior Member Join Date: Apr 2013 Posts: 9 *ANSWER* Stuck on #4

To calculate I generated several data sets each of two points where y=sin(pi*x). For each dataset, I generated a hypothesis (a slope a) that minimized the squared error for each of the two points. I did this by calculating the error as , differentiating with respect to a, setting the result to zero and solving for a. This gave me . If I then average my per-dataset slopes (the a's), I get 1.42.

This seems wrong, not only as it's not an available choice ( ) but also because it does not yield a smaller bias than, for example, .79.

I've seen suggestions to use linear regression to calculate the a's, but I don't think that's where I'm going wrong (not only that, but I'm not sure how to do the linear regression without an intercept term).
#2 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478 Re: *ANSWER* Stuck on #4

Quote:
 Originally Posted by mvellon This seems wrong, not only as it's not an available choice ( ) but also because it does not yield a smaller bias than, for example, .79.
Your procedure is correct. Just to address the above point without commenting on the correctness of your calculation, there is an available choice for your answer, and there is no requirement that the slope is less than 0.79.
__________________
Where everyone thinks alike, no one thinks very much
#3
 marek Member Join Date: Apr 2013 Posts: 31 Re: *ANSWER* Stuck on #4

For what it's worth, I think you're calculating 4 correctly. After 10^6 runs, my average a was 1.4301. It was unsettling to not see my answer among those listed, especially since the others depend on correctly interpreting this question. It would be nice to get further corroboration, simply because none of the above doesn't mean 1.43 was correct.

However, I believe your bias calculation may be off, as your conclusion is different than what I obtained despite having roughly the same a.
#4
 jcmorales1564 Member Join Date: Apr 2013 Posts: 12 Re: *ANSWER* Stuck on #4

I calculated it in two different ways and I get a consistent answer that is higher than answer [d] (0.79x). I am unsure as to how far away the answer must be to consider it answer [e] ("None of the Above")?

The difference between answers [c] and [d] is 0.34x. May I assume that if my answer is 1.13x or above (from 0.79x + 0.34x = 1.13x) then [e] "None of the above" is the correct answer (and viceversa)?

I need guidance as to how to determine, in general, how far is "far away" so that I can decide between answers [d] and [e].

Thank you.

Juan
#5
 IsidroHidalgo Member Join Date: Apr 2013 Location: Toledo (Spain) Posts: 28 Re: *ANSWER* Stuck on #4

Juan, after the derivative of the mean squarred error have you arrived to ?
If so, answer is IMO (I haven't send my answers) clearly upon 0.79
Good luck!
Isidro
#6
 IsidroHidalgo Member Join Date: Apr 2013 Location: Toledo (Spain) Posts: 28 Re: *ANSWER* Stuck on #4

Quote:
 Originally Posted by mvellon To calculate I generated several data sets each of two points where y=sin(pi*x). For each dataset, I generated a hypothesis (a slope a) that minimized the squared error for each of the two points. I did this by calculating the error as , differentiating with respect to a, setting the result to zero and solving for a. This gave me . If I then average my per-dataset slopes (the a's), I get 1.42. This seems wrong, not only as it's not an available choice ( ) but also because it does not yield a smaller bias than, for example, .79. I've seen suggestions to use linear regression to calculate the a's, but I don't think that's where I'm going wrong (not only that, but I'm not sure how to do the linear regression without an intercept term).
I think you have a typo, is'n it? For me  #7
 Ziad Hatahet Member Join Date: Apr 2013 Location: San Francisco, CA Posts: 23 Re: *ANSWER* Stuck on #4

Quote:
 Originally Posted by IsidroHidalgo I think you have a typo, is'n it? For me  Yes, that's what I got too. So you're saying that with using this formula, you're getting 0.79, and not 1.42 as mentioned in a couple of other threads?
#8
 IsidroHidalgo Member Join Date: Apr 2013 Location: Toledo (Spain) Posts: 28 Re: *ANSWER* Stuck on #4

Not at all. Using this a I obtain 1.42...
#9 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478 Re: *ANSWER* Stuck on #4

Quote:
 Originally Posted by jcmorales1564 I am unsure as to how far away the answer must be to consider it answer [e] ("None of the Above")?
Your answer should agree with the given answer to two-decimal-digit accuracy as stated in the problem, or else be considered "none of the above."
__________________
Where everyone thinks alike, no one thinks very much
#10
 jcmorales1564 Member Join Date: Apr 2013 Posts: 12 Re: *ANSWER* Stuck on #4

I also obtain 1.42 with the formula you mention which is based on deriving WRT "a" and equalling to zero to minimize. I also calculated 1.4 by finding the "a" for each value of x1 and x2 and then selecting the "a" associated with the smaller mean squared error.

The answer (a = 1.4), which is higher than the case discussed in class, makes sense to me because the line is forced to pass through zero. It can only rotate about the origin. It removes the translational degree of freedom that would otherwise be available when the intercept is included (y = ax + b). In that latter case any two points are used to create the line (the case discussed in class), and there is a high probability of obtaining many more cases with slope close to zero so I would expect "a" to be lower when using y=ax + b (after calculating the average of many cases). It also makes sense that b tends to zero.

Supposing 1.42 is the correct value, should it be [d] or [e]?

To "d", or not to "d", that is the question  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
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home General     General Discussion of Machine Learning     Free Additional Material         Dynamic e-Chapters         Dynamic e-Appendices Course Discussions     Online LFD course         General comments on the course         Homework 1         Homework 2         Homework 3         Homework 4         Homework 5         Homework 6         Homework 7         Homework 8         The Final         Create New Homework Problems Book Feedback - Learning From Data     General comments on the book     Chapter 1 - The Learning Problem     Chapter 2 - Training versus Testing     Chapter 3 - The Linear Model     Chapter 4 - Overfitting     Chapter 5 - Three Learning Principles     e-Chapter 6 - Similarity Based Methods     e-Chapter 7 - Neural Networks     e-Chapter 8 - Support Vector Machines     e-Chapter 9 - Learning Aides     Appendix and Notation     e-Appendices

All times are GMT -7. The time now is 06:13 AM.

 Contact Us - LFD Book - Top

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. 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.