I am reading this tuorial on constrastive divergence and at the end of page 2 they define the expectation given the data. I am unclear on what this means? How is this different from regular expected value?

  • $\begingroup$ Maybe they just mean the empirical mean? $\endgroup$ – kjetil b halvorsen Dec 16 '16 at 12:21
  • $\begingroup$ of the sample ? $\endgroup$ – user2879934 Dec 16 '16 at 13:06
  • $\begingroup$ It would be helpful to put the relevant equations in the question. In general "expected value given the data" would refer to a combination of this and this. $\endgroup$ – GeoMatt22 Dec 16 '16 at 14:25
  • $\begingroup$ If I have found the part you mean, you misquote what it says there. It doesn't say "given the data" it says "given the data distribution". The distinction is important. $\endgroup$ – Glen_b Dec 16 '16 at 23:33
  • $\begingroup$ What is the distinction $\endgroup$ – user2879934 Dec 17 '16 at 0:47

In that context, it is still referring to a population mean.

The distribution F(X) in the question has population parameter vector $\Theta$. It's just a nonstandard notation.


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