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-   -   Description on page 55 (http://book.caltech.edu/bookforum/showthread.php?t=4118)

junjy 03-17-2013 07:00 PM

Description on page 55
 
First, a general comment: Prof. Abu-Mostafa made things really really clear, my million thanks!

Here I have a small confusion: On p.55, line 6, it says "(What the growth function ...), so we can get a factor similar to the '100' in the above example".

The analogy makes the general idea 100 times more comprehensible than plunging into the proof directly. However, here I minded a gap. Can anybody help if this is my misunderstanding or I am right in this point :clueless:?

- the '100' is a "good" guy in the above example, which "condenses" (so shrink) the coloured area that times much.
- the growth function, on the other hand, is a bad guy, which gives that much ways for hypotheses behaving differently on the canvas, and "smears" the colours

So I think they are more inversely comparable, e.g. if the example is given as follows:

However many hypotheses in \mathcal{H}, then can only behave in m ways. Therefore, each point on the canvas that is coloured will be coloured M/m times.

yaser 03-17-2013 11:24 PM

Re: Description on page 55
 
Quote:

Originally Posted by junjy (Post 9986)
First, a general comment: Prof. Abu-Mostafa made things really really clear, my million thanks!

Here I have a small confusion: On p.55, line 6, it says "(What the growth function ...), so we can get a factor similar to the '100' in the above example".

The analogy makes the general idea 100 times more comprehensible than plunging into the proof directly. However, here I minded a gap. Can anybody help if this is my misunderstanding or I am right in this point :clueless:?

- the '100' is a "good" guy in the above example, which "condenses" (so shrink) the coloured area that times much.
- the growth function, on the other hand, is a bad guy, which gives that much ways for hypotheses behaving differently on the canvas, and "smears" the colours

So I think they are more inversely comparable, e.g. if the example is given as follows:

However many hypotheses in \mathcal{H}, then can only behave in m ways. Therefore, each point on the canvas that is coloured will be coloured M/m times.

You are correct in the characterization of good and bad guys. The redundancy accounting through factors like 100 is just a technical way to get a handle on the growth function, so indeed they work in opposite directions.

junjy 03-19-2013 01:51 AM

Re: Description on page 55
 
Thank you for the clearance!


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