LFD Book Forum Noisy target - problem in understanding distribution
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#1
06-19-2015, 03:25 AM
 iamds Junior Member Join Date: Jun 2015 Posts: 2
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 ?
#2
06-19-2015, 11:17 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,476
Re: Noisy target - problem in understanding distribution

Quote:
 Originally Posted by iamds 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 .
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#3
05-12-2016, 02:20 AM
 waleed Junior Member Join Date: May 2016 Posts: 5
Re: Noisy target - problem in understanding distribution

Quote:
 Originally Posted by yaser 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

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