LFD Book Forum  

Go Back   LFD Book Forum > Course Discussions > Online LFD course > Homework 4

Reply
 
Thread Tools Display Modes
  #1  
Old 01-31-2013, 01:01 PM
geekoftheweek geekoftheweek is offline
Member
 
Join Date: Jun 2012
Posts: 26
Default questions 5 & 6

Once we find an average hypothesis, we have to compute bias=E_x[bias(x)] and var=E_x[var(x)]. In order to compute the expectation values of bias/var wrt x, I assume we need to generate a *new* set of points. Correct? How big should that set be?
Reply With Quote
  #2  
Old 01-31-2013, 02:45 PM
geekoftheweek geekoftheweek is offline
Member
 
Join Date: Jun 2012
Posts: 26
Default Re: questions 5 & 6

...or are we just supposed to use the points generated in order to calculate g_bar? That would mean that bias and var have twice as many points to average over than the number of data sets used to calculate g_bar, because each data set had two two data points.
Reply With Quote
  #3  
Old 01-31-2013, 04:23 PM
sanbt sanbt is offline
Member
 
Join Date: Jan 2013
Posts: 35
Default Re: questions 5 & 6

So to calculate g_bar you used 2 points to get each hypothesis and average over them.

Now Bias and var should come from the entire range of the real line. I would say
about hundreds range from -1 to 1.
Reply With Quote
  #4  
Old 02-01-2013, 11:26 AM
geekoftheweek geekoftheweek is offline
Member
 
Join Date: Jun 2012
Posts: 26
Default Re: questions 5 & 6

Quote:
Originally Posted by sanbt View Post
Now Bias and var should come from the entire range of the real line. I would say
about hundreds range from -1 to 1.
Are you saying generate 100 new points?
Reply With Quote
  #5  
Old 02-01-2013, 05:57 PM
sanbt sanbt is offline
Member
 
Join Date: Jan 2013
Posts: 35
Default Re: questions 5 & 6

Quote:
Originally Posted by geekoftheweek View Post
Are you saying generate 100 new points?
yes
Reply With Quote
  #6  
Old 02-01-2013, 10:30 PM
gah44 gah44 is offline
Invited Guest
 
Join Date: Jul 2012
Location: Seattle, WA
Posts: 153
Default Re: questions 5 & 6

All these are approximating integrals.

Many problems really are sums, but this one is, theoretically, continuous.

First you do 2D integrals to compute a, a 1D integral to compute bias,
and a 3D integral to compute variance.

(I think it would also work to compute bias+variance in the first place, and subtract bias to get variance, but I didn't try that.)

I used equally space points for all, but you could also use random points.

If I was in the right mood, I might have done Gaussian quadrature, or some other numerical integration method.
Reply With Quote
Reply

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 02:55 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.