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-   -   Exercise 1.7 (http://book.caltech.edu/bookforum/showthread.php?t=4482)

netweavercn 04-20-2014 05:00 PM

Exercise 1.7
 
A little confused about 1.7. what is the purpose of this exercise: learning is impossible?

in (a), both hypotheses have 1 agree on all 3 points and no agree on all other 7 cases. so which hypothesis should be chose by learning algorithm? as the 2 hypotheses are the same.

in(b), still same situation

in(c), there are 4 cases agrees.

(d), is it possible to agree all 8 cases?

magdon 04-21-2014 11:21 AM

Re: Exercise 1.7
 
The purpose of the exercise is to show what can possibly happen outside the data, namely anything, and it is the same no matter how you pick your g from the data.

Compare this with the bin in the next section. What can possibly remain in the bin after you pick your sample is every possible combination of red and green marbles.

So it is always *possible* to end up with a hypothesis that is arbitrarily bad no matter what algorithm you use to pick that hypothesis using only the data as a guide. That is what thiis exercise illustrates. In the next section you will learn that while anything is possible, some things are more likely than others.

Quote:

Originally Posted by netweavercn (Post 11671)
A little confused about 1.7. what is the purpose of this exercise: learning is impossible?

in (a), both hypotheses have 1 agree on all 3 points and no agree on all other 7 cases. so which hypothesis should be chose by learning algorithm? as the 2 hypotheses are the same.

in(b), still same situation

in(c), there are 4 cases agrees.

(d), is it possible to agree all 8 cases?

You may have misunderstood the question. In (a) you pick the hypothesis that is always \bullet, since that is what agrees with the data the most (from the table on the same page). Compare this g with the possible choices for f given by f_1,\ldots,f_8: 1 agrees with g on all three test points; 3 agree with g on two test points; 3 agree with g on one test points; 1 agrees with g on none of the test points;

netweavercn 04-22-2014 04:03 PM

Re: Exercise 1.7
 
Thanks a lot, so for (a), whatever you choose which h (white or black), the result is the same.


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