LFD Book Forum Page 63 and excercise 2.8

#1
09-28-2014, 03:51 PM
 cbmachine Junior Member Join Date: Sep 2014 Posts: 3
Page 63 and excercise 2.8

On page 63 its given that g_(x) is approximately the mean of all gk(x) for any x. Why is it an estimate and not exactly the mean?

Since g_(x) is the average for any x, then its possible for it to have non binary values for a binary classification problem. But this seems to be a bit counter intuitive to me. Can you please clarify if my understanding of g_(x) is correct
#2
10-01-2014, 05:43 PM
 Newbrict Junior Member Join Date: Sep 2014 Posts: 1
Re: Page 63 and excercise 2.8

I think because it's computed over a finite set of points, whereas the actual value for is an exact solution
#3
10-02-2014, 08:17 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Page 63 and excercise 2.8

because is defined as an expectation with respect to data sets of g(x). The average over data sets approximates this expectation.

Yes, is not a valid hypothesis: it may not be in your hypothesis set; it may not even be binary. It is never used as a classifier. It is just used to represent "what would happen on average after learning", and this abstract function plays a role in defining the bias in the bias variance decomposition.

Quote:
 Originally Posted by Newbrict I think because it's computed over a finite set of points, whereas the actual value for is an exact solution
__________________
Have faith in probability

 Thread Tools Display Modes Linear 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 10:53 PM.