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-   -   Noisy target - problem in understanding distribution (http://book.caltech.edu/bookforum/showthread.php?t=4607)

iamds 06-19-2015 03:25 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 06-19-2015 11:17 PM

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 f({\bf x}) as a distribution P(y|{\bf x}) is based on using a "delta function" which allows distributions to put all the probability on a single value of y, thus making it effectively a function since y is uniquely determined by {\bf x}.

waleed 05-12-2016 02:20 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 f({\bf x}) as a distribution P(y|{\bf x}) is based on using a "delta function" which allows distributions to put all the probability on a single value of y, thus making it effectively a function since y is uniquely determined by {\bf x}.

thank you yaser


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