LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Chapter 2 - Training versus Testing (http://book.caltech.edu/bookforum/forumdisplay.php?f=109)
-   -   Questions on Probability (http://book.caltech.edu/bookforum/showthread.php?t=407)

 pventurelli@gotoibr.com 04-28-2012 08:02 PM

Questions on Probability

I have a question on the use of the Expectation Value operation as used in the class and the book.

My (simplistic) understanding of the expectation value of a quantity is basically like taking a weighted average: for random variable X with probability distribution Pr(X) the expectation value would be either a sum (if X is discrete) or an integral (X is continuous) over all X values of X_i * Pr(X=X_i). And then I would multiply everything by a 1/N or a 1/Delta(X).

Is this more or less what is meant in the class by the E[] notation? Maybe I just need to become more comfortable using this operation, however language like that on page 61 of the book where the in sample error is defined as an averaging procedure in (implied?) contrast to the definition of E_out leaves me confused. Isn't expectation a weighted average *by definition*?

Thanks for your help!

 yaser 04-28-2012 08:38 PM

Re: Questions on Probability

Quote:
 Originally Posted by pventurelli@gotoibr.com (Post 1657) I have a question on the use of the Expectation Value operation as used in the class and the book. My (simplistic) understanding of the expectation value of a quantity is basically like taking a weighted average: for random variable X with probability distribution Pr(X) the expectation value would be either a sum (if X is discrete) or an integral (X is continuous) over all X values of X_i * Pr(X=X_i). And then I would multiply everything by a 1/N or a 1/Delta(X). Is this more or less what is meant in the class by the E[] notation? Maybe I just need to become more comfortable using this operation, however language like that on page 61 of the book where the in sample error is defined as an averaging procedure in (implied?) contrast to the definition of E_out leaves me confused. Isn't expectation a weighted average *by definition*? Thanks for your help!
The sample average can be technically posed as an expected value (by giving each example a probability 1/N). However, the correct way of thinking about is that it is a random variable (the source of randomization being which data set was generated) rather than an expected value like . However it is a random variable obtained by averaging a (hopefully) large number of sample points, and as such its value will tend to be close to the expected value per the laws of large numbers.

 All times are GMT -7. The time now is 10:06 PM.

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2019, 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.