Re: Discussion of the VC proof
I have also another question on the same page (190):
At the end of the page there is the formula: https://latex.codecogs.com/gif.latex...pace;S&space;] I don't understand why the RHS is greater or equal to the LHS. The only legitimation I see for this is, that the distribution of P[S] is uniform, but this has not been stated in the text. Or do I oversee here anything and this is also valid for all kinds of distribution? 
Re: Discussion of the VC proof
Quote:
When we have a uniform distribution of P[S] the outcome of the productsum is simply the average of all P[AS], since And an average is of course less than or equal to the maximum of P[AS]. If P[S] is not distributed uniformly we still have an average, but a weighted average. But also here the result is always less than or equal to the maximum. Because you cannot find weighting factors that are in sum 1 but will lead to a higher result as the maximum P[AS]. 
Re: Discussion of the VC proof
Correct.
Quote:

Re: Discussion of the VC proof
You are correct. We could have made other assumptions.
But there is a special reason why we DO want 1. Because we are bounding the probability, and so there is nothing to prove if we claim that a probability is less equal to 1. So, whenever the RHS (i.e. the bound) evaluates to 1 or bigger, there is nothing to prove. So we only need to consider the case when the bound evaluates to less than 1. Quote:

Re: Discussion of the VC proof
Thank you very much for your answers. This helps me a lot to understand the intention of the single steps of this prove.

Re: Discussion of the VC proof
i had same question but thanks to your website my question just solved. thanks

Re: Discussion of the VC proof
thank you for your answer. i like it.

Re: Discussion of the VC proof
at the beginning everything was complicated, so at first, I gave it a thought, but I could take in nothing. by the way that was pretty easy. thank you so much.

All times are GMT 7. The time now is 08:53 AM. 
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. AbuMostafa, Malik MagdonIsmail, and HsuanTien Lin, and participants in the Learning From Data MOOC by Yaser S. AbuMostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.