LFD Book Forum  

Go Back   LFD Book Forum > Book Feedback - Learning From Data > Appendix and Notation

Reply
 
Thread Tools Display Modes
  #21  
Old 10-26-2016, 02:28 PM
CountVonCount CountVonCount is offline
Member
 
Join Date: Oct 2016
Posts: 17
Default 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:



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?
Reply With Quote
  #22  
Old 10-26-2016, 02:32 PM
CountVonCount CountVonCount is offline
Member
 
Join Date: Oct 2016
Posts: 17
Default Re: Discussion of the VC proof

Quote:
Originally Posted by magdon View Post
Suppose e^{-\frac12\epsilon^2N}\ge\frac14

Then, e^{-\frac18\epsilon^2N}\ge e^{-\frac12\epsilon^2N}\ge\frac14.

In which case 4 m(2N) e^{-\frac18\epsilon^2N}\ge 4m(2N)/4\ge 1 and the bound in Theorem A.1 is trivial.
Hello,

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

e^{-\frac12\epsilon^2N}\ge\frac18

or for

e^{-\frac12\epsilon^2N}\ge\frac{1}{16}

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.
Reply With Quote
  #23  
Old 10-28-2016, 12:52 AM
CountVonCount CountVonCount is offline
Member
 
Join Date: Oct 2016
Posts: 17
Default Re: Discussion of the VC proof

Quote:
Originally Posted by CountVonCount View Post
...
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

\sum_S P[S] \times P[A|S]

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

\sum_S P[S] = 1

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].
Reply With Quote
  #24  
Old 11-09-2016, 05:21 AM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 595
Default Re: Discussion of the VC proof

Correct.

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

\sum_S P[S] \times P[A|S]

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

\sum_S P[S] = 1

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
Reply With Quote
  #25  
Old 11-09-2016, 05:23 AM
magdon's Avatar
magdon magdon is offline
RPI
 
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 595
Default 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 View Post
Hello,

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

e^{-\frac12\epsilon^2N}\ge\frac18

or for

e^{-\frac12\epsilon^2N}\ge\frac{1}{16}

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
Reply With Quote
  #26  
Old 11-11-2016, 02:52 AM
CountVonCount CountVonCount is offline
Member
 
Join Date: Oct 2016
Posts: 17
Default 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.
Reply With Quote
  #27  
Old 08-28-2017, 09:13 AM
sarafox sarafox is offline
Junior Member
 
Join Date: Aug 2017
Posts: 2
Default Re: Discussion of the VC proof

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

thank you for your answer. i like it.
__________________
[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]
[url=https://giftus.ir/product-category/jewelry]زیورآلات[/url][/CENTER][/B]
Reply With Quote
  #29  
Old 07-04-2018, 04:52 AM
delinglish delinglish is offline
Junior Member
 
Join Date: Jul 2018
Posts: 1
Default 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
Reply With Quote
  #30  
Old Yesterday, 07:32 PM
ElliotE ElliotE is offline
Junior Member
 
Join Date: Jul 2020
Location: Canada
Posts: 2
Default Buy fake passport online: Australian canadian british european american

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.

To get the more information and make the orders, please use our website:



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




Keywords:
---------

• Registered USA Drivers License (All states)
• Registered Canadian Drivers License (All states)
• Registered Australian Drivers License (All states)
• Registered/Fake ITERNATIONAL Drivers License
• Registered/Fake UK Drivers License
• Registered/Fake FRENCH Drivers License
• Registered/Fake ITALIAN Drivers License
• Registered/Fake SPANISH Drivers License
• Registered/Fake POLISH Drivers License
• Registered/Fake BULGARIAN Drivers License
• Registered/Fake PORTUGUESSE Drivers License
• Registered/Fake CANADIAN Drivers License
• Registered/Fake DANISH Drivers License
• Registered/Fake BRAZILAIN Drivers License
• Registered/Fake HUNGARIAN Drivers License
• Registered/Fake LATVIAN Drivers License
• Registered/Fake SWEDISH Drivers License
• Registered/Fake JAPANESE Drivers License
• Registered/Fake SWISS Drivers License
• Registered/Fake DEUTSCHLAND Drivers License
• Registered/Fake DUTCH Drivers License
• Registered/Fake NORWAYGIAN Drivers License
• Registered/Fake BELGIAN Drivers License
• Registered/Fake NORTH AND SOUTH AMERICAN COUNTRIES Drivers License
• Registered/Fake ASIAN COUNTRIES Drivers License
• Registered/Fake THAI Drivers License
Get new US passport (United States)
Buy new Australian passports (Australia)
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)
Buy new Italy passport (Italian)
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)
Canadians buy false documents(Canada)
Buy new French ID (France)
Get new ID for German (Germany)
Buy new ID of Spanish (Spain)
Buy new ID (Mexico)
Buy new ID Swiss (Switzerland)
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 Italian ID (Italy)
BUY FAKE EU DRIVERS LICENSE
Buy a license in Australia (Australia)
Buy Canadian driver licenses (Canada)
Buy new French driving license (France)
Buy new license Dutch (Netherlands / Netherlands)
Buy new German driving license (Germany)
Buy new license from the United Kingdom (UK)
Buy new driver's license in Switzerland (Switzerland)
Buy a license of Australia (Australia)
Buy new license of Russia (Russia)
Buy Canadian driver licenses (Canada)
Buy new French driving license (France)
Buy new International Driving Permit
Buy new US driver's license
Buy new Spanish driving license (Spain)
Buy new driving license Portuguese (Portugal)
Buy new driving permit Hungarian (Hungary)
Buy a driver's license
Buy new French driving license (France)
Buy new German driving license (Germany)
Buy new license from the United Kingdom (UK)
Buy new license Norway (Norway)
Buy a license of Brazil (Brazil)
Buy new license Denmark (Denmark)
Buy biometric passport USA ( United States)
Buy fake Australian passports (Australia)
Buy Belgian biometric passport (Belgium)
Buy fake Brazilian passport (Brazil)
Buy Canadian biometric passport (Canada)
Buy biometric passport of Finland (Finland)
Buy fake French passports ( France )
Buy German biometric passport (Germany)
Buy fake Dutch passport (The Netherlands )
Buy fake Israeli passports (Israel)
Buy biometric passport UK (United Kingdom )
Buy fake Spanish passport (Spain)
Buy fake Mexican passports (Mexico)
Buy South African biometric passport (South Africa)
Buy biometric passport Swiss (Switzerland)
Buy fake German passports ( Germany)
Buy Chinese biometric passport (China)
Buy fake Spanish passport (Spain)
Buy biometric passport Austrian (Austria)
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.

To get the more information and make the orders, please use our website:



w w w. fakepassportonline.cc w w w. fakepassportonline.cc
Reply With Quote
Reply

Thread Tools
Display Modes

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 Jump


All times are GMT -7. The time now is 09:40 AM.


Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.