LFD Book Forum - Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target Func

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- - Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target Func (http://book.caltech.edu/bookforum/showthread.php?t=4653)

Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target Func

Hello, I am confused by the meaning of these four words:

Noisy Target vs Target Distribution

I understand that a target distribution is a probability distribution, but how about noisy target? What is a noisy target? A value or a function or a probability distribution?

Deterministic Target vs Deterministic Target Function

Same above, I understand that a deterministic target function is a function, but how about deterministic target? A value or a function?

And...

Quote:

Noisy target = deterministic target f(x) = E(y|x) plus noise y − f(x)

Is y here a value or a function?

I am very confused... :(

Thank you very much for your time spending on here.

Re: Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target

Apologies for the confusion.

Noisy target and deterministic target refer to a specific target value (for example at a specific point x). So you have a data point (x,y).

If y=f(x), we say that y is a deterministic target and f is a deterministic target function.

If for the same value of x you may observe different values of y (the example in the book: several people may have the same income but some may default on credit debt and some may not), then we say that y is a noisy target - its value is not deterministically determined given x. The way we model this situation is using a target distribution P[y|x]. So P[y|x] is the distribution of the (noisy) target, and we call it the target distribution.

Hope this helps.

Quote:

Originally Posted by ntvy95 (Post 12246)

Re: Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target

Quote:

Originally Posted by magdon (Post 12249)

Apologies for the confusion.

Noisy target and deterministic target refer to a specific target value (for example at a specific point x). So you have a data point (x,y).

If y=f(x), we say that y is a deterministic target and f is a deterministic target function.

If for the same value of x you may observe different values of y (the example in the book: several people may have the same income but some may default on credit debt and some may not), then we say that y is a noisy target - its value is not deterministically determined given x. The way we model this situation is using a target distribution P[y|x]. So P[y|x] is the distribution of the (noisy) target, and we call it the target distribution.

Hope this helps.

So y here serves as a (random) variable?

Re: Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target

Quote:

Originally Posted by ntvy95 (Post 12252)

So y here serves as a (random) variable?

As the book says: "Instead of y=f(x), we can take the output y to be a random variable..."

Re: Noisy Target vs Target Distribution,Deterministic Target vs Deterministic Target

Quote:

Originally Posted by MaciekLeks (Post 12264)

As the book says: "Instead of y=f(x), we can take the output y to be a random variable..."

Man, thank you. I have missed that important point. :'(