LFD Book Forum Discussion of the VC proof

#21
10-26-2016, 02:28 PM
 CountVonCount Member Join Date: Oct 2016 Posts: 17
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:

$\sum_S&space;\mathbb{P}[S]\times\mathbb{P}[sup_{h\in&space;H}\vert&space;E_{in}(h)&space;-&space;{E_{in}}'(h))&space;\vert&space;>&space;\frac{\varepsilon&space;}{2}]&space;\leq&space;sup_S&space;\mathbb{P}[sup_{h\in&space;H}\vert&space;E_{in}(h)&space;-&space;{E_{in}}'(h))&space;\vert&space;>&space;\frac{\varepsilon&space;}{2}]&space;\vert&space;S&space;]$

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?
#22
10-26-2016, 02:32 PM
 CountVonCount Member Join Date: Oct 2016 Posts: 17
Re: Discussion of the VC proof

Quote:
 Originally Posted by magdon Suppose Then, . In which case and the bound in Theorem A.1 is trivial.
Hello,

thanks for the answer. I understand this argument, however this holds also for

or for

Thus the value 1/4 is somehow magic for me.

Edit: I think you choose 1/4 because it is so easy to see, that the RHS of Theorem A.1 gets 1. Nevertheless with a different value you would get a different outcome of the final formula.
#23
10-28-2016, 12:52 AM
 CountVonCount Member Join Date: Oct 2016 Posts: 17
Re: Discussion of the VC proof

Quote:
 Originally Posted by CountVonCount ... 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?
I got it by myself.
When we have a uniform distribution of P[S] the outcome of the product-sum

is simply the average of all P[A|S], since

And an average is of course less than or equal to the maximum of P[A|S].
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[A|S].
#24
11-09-2016, 05:21 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Discussion of the VC proof

Correct.

Quote:
 Originally Posted by CountVonCount I got it by myself. When we have a uniform distribution of P[S] the outcome of the product-sum is simply the average of all P[A|S], since And an average is of course less than or equal to the maximum of P[A|S]. 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[A|S].
__________________
Have faith in probability
#25
11-09-2016, 05:23 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
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:
 Originally Posted by CountVonCount Hello, thanks for the answer. I understand this argument, however this holds also for or for Thus the value 1/4 is somehow magic for me. Edit: I think you choose 1/4 because it is so easy to see, that the RHS of Theorem A.1 gets 1. Nevertheless with a different value you would get a different outcome of the final formula.
__________________
Have faith in probability
#26
11-11-2016, 02:52 AM
 CountVonCount Member Join Date: Oct 2016 Posts: 17
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.
#27
08-28-2017, 09:13 AM
 sarafox Junior Member Join Date: Aug 2017 Posts: 2
Re: Discussion of the VC proof

i had same question but thanks to your website my question just solved. thanks
__________________
https://seofox.ir
#28
04-23-2018, 08:00 AM
 samyar1 Junior Member Join Date: Apr 2018 Location: iran Posts: 1
Re: Discussion of the VC proof

__________________
[B][CENTER][URL="http://www.sitranet.com/store-design-package"]طراحی فروشگاه اینترنتی[/URL]
[URL="http://www.sitranet.com/seo-pack"]سئو فروشگاه اینترنتی[/URL]
#29
07-04-2018, 04:52 AM
 delinglish Junior Member Join Date: Jul 2018 Posts: 1
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.
__________________
delinglish.com
#30
Yesterday, 07:32 PM
 ElliotE Junior Member Join Date: Jul 2020 Location: Canada Posts: 2

w w w. fakepassportonline.cc - the authentic registered and unregistered documents provider. We produce real and fake passport, drivers license, stamps, visa id cards, IELTS Certificates, novelty documents, counterfeit identity card, identification documents, driver’s license, SSN card for different countires: USA, Italy, Australia, Belgium, Brazil, Canada, Finland, France, Germany, Netherlands,Spain, United Kingdom, Malaysia, Norway, Switzerland. We process only high quality full citizenship documents.

Buy high quality real fake passports from w w w. buyrealdocuments.cc and expand new rights and freedom. A second real passports opens doors offshore otherwise closed to many countries citizens. Best of all, dual citizenship and a second passports can be new key to reduced taxes and increased asset protection and it could even protect new life. For a citizen of a totalitarian country or one that holds a passport with poor visa-free travel it means complete freedom of movement along with the right to live and work in a normal developed society.

We produce real and novelty documents of all types. All of our products are printed on high-quality printing machines, they have valid holograms, secret features, and have been passed under UV light and other verification equipment. Rest assured that new documents are 100% real and registered.

w w w. fakepassportonline.cc w w w. fakepassportonline.cc

Keywords:
---------

• Registered USA Drivers License (All states)
• Registered Australian Drivers License (All states)
• Registered/Fake NORTH AND SOUTH AMERICAN COUNTRIES Drivers License
• Registered/Fake ASIAN COUNTRIES Drivers License
Get new US passport (United States)
Get new Belgian passport (Belgium)
Get new passports from the United Kingdom (UK)
Get new passport from Hungary (Hungary)
Get new passport from Australia (Australia)
Get new passport of Denmark (Denmark)
Get new Polish passport (Poland)
Buy new ID cards in European Union
Buy new ID US (United States)
Buy new ID of Australia (Australia)
Buy new ID of Belgium (Belgium)
Buy new ID of Brazil (Brazil)
Get new ID for German (Germany)
Buy new ID of Spanish (Spain)
Get new ID for German (Germany)
Buy new ID of Hungary (Hungary)
Buy new ID of Australia (Australia)
Buy new ID of Brazil (Brazil)
Buy new driving permit Hungarian (Hungary)
Buy biometric passport USA ( United States)
Buy biometric passport of Finland (Finland)
Buy fake French passports ( France )
Buy fake Dutch passport (The Netherlands )
Buy biometric passport UK (United Kingdom )
Buy South African biometric passport (South Africa)
Buy fake German passports ( Germany)
Buy fake Asian passports ( Japan, Malaysian, Singapore, Chinese, Thailand, Vietnam, Philippines)
Buy Fake Passport, False Passport, Passport, ID card, Cards, UK, Sell, Online, driving license, birth certificate, diplomas, Canadian, British, Sale, Novelty, Counterfeit, real, American, United, States, USA, US, Italian, Malaysian, Australian, Documents,Identity, Identification, Driver's License, License, Driver's, Residence, Permit, SSN , ID, Free , Identity Theft, Fake, Novelty, Camouflage, Anonymous, Private , Safe, Travel, International, Offshore, Banking, ID, Driver, Drivers, License, Instant, Online, For Sale, Cheap, Wholesale, New Identity, Citizenship, Identity, Identification, Fake Documents, Diplomatic, Nationality, How to make, novelty, id.

w w w. fakepassportonline.cc w w w. fakepassportonline.cc

 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 12:27 PM.