LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Chapter 1 - The Learning Problem (http://book.caltech.edu/bookforum/forumdisplay.php?f=108)
-   -   Noisy target - problem in understanding distribution (http://book.caltech.edu/bookforum/showthread.php?t=4607)

 iamds 06-19-2015 04:25 AM

Noisy target - problem in understanding distribution

Noisy targets:

Quote:
 " Indeed, we can formally express any function f as a distribution P (y I x) by choosing P (y I x) to be zero for all y except y = f (x) . Therefore, there is no loss of generality if we consider the target to be a distribution rather than a function"
I am not able to understand how is no loss in generality ensured by considering target distribution and not target function ?

 yaser 06-20-2015 12:17 AM

Re: Noisy target - problem in understanding distribution

Quote:
 Originally Posted by iamds (Post 11976) I am not able to understand how is no loss in generality ensured by considering target distribution and not target function ?
If we can express a function as a distribution, then considering only distributions will not exclude functions, hence there would be no loss in generality. The fact that we can indeed express a function as a distribution is based on using a "delta function" which allows distributions to put all the probability on a single value of , thus making it effectively a function since is uniquely determined by .

 waleed 05-12-2016 03:20 AM

Re: Noisy target - problem in understanding distribution

Quote:
 Originally Posted by yaser (Post 11977) If we can express a function as a distribution, then considering only distributions will not exclude functions, hence there would be no loss in generality. The fact that we can indeed express a function as a distribution is based on using a "delta function" which allows distributions to put all the probability on a single value of , thus making it effectively a function since is uniquely determined by .
thank you yaser

 All times are GMT -7. The time now is 12:35 AM.