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Old 01-07-2019, 11:36 PM
Fromdusktilldawn Fromdusktilldawn is offline
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Join Date: Sep 2017
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Default What is the definition of expectation with respect to data set

In probability class, we take expectation with respect to random variables with a certain probability distribution.

Suppose that X ~ N(mu,sigma^2) is a Gaussian random variable.

Then E[X] = mu, the mean of the Gaussian random variable, which can be show by performing expectation integral of the Gaussian distribution.

In the book, D is a set of pair of values {(x_n,y_n)}, not a random variable. Even if it is a random variable, its distribution is unknown.

Then what does does the symbol E_D or E_D_val mean?

What is the random variable here? Is it g, g^-, x_n, y_n, or (x_n,y_n) or e(g^-(x_n),y_n)?

And these random variables to generated according to what probability distribution?

This is the only part of the book that is confusing for me. Please clarify what it means to take expectation with respect to a set.
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