Contents
Which is the formula for the conditional variance?
we define the conditional variance Var(Y|X) = E([Y – E(Y|X)]2 | X) (Note that both expected values here are conditional expected values.) What does this say in words (and pictures)? Exercise: Derive another formula for the conditional variance, analogous to the second formula for the marginal variance. (And say it in words!)
Why does the discriminator get worse as the generator gets better?
The utopian situation where both networks stabilize and produce a consistent result is hard to achieve in most cases. One explanation for this problem is that as the generator gets better with next epochs, the discriminator performs worse because the discriminator can’t easily tell the difference between a real and a fake one.
How is conditioning done in Gan loss function?
The conditioning is usually done by feeding the information y into both the discriminator and the generator, as an additional input layer to it. The following modified loss function plays the same min-max game as in the Standard GAN Loss function.
How to calculate conditional covariance between Y I and Y J?
Conditional Covariance Let Y i and Y j denote two variables of interest, and let X denote a vector of variables on which we wish to condition. Then the conditional covariance between Y i and Y j given that X = x is σ i, j. x = cov (Y i, Y j | X=x) = E { (Y i − μ Y i.
How are unconditional and conditional variances collected in a matrix?
Just as the unconditional variances and covariances can be collected into a variance-covariance matrix Σ, the conditional variances and covariances can be collected into a conditional variance-covariance matrix: Note!
Which is the conditional mean of Y given x = x?
Then the conditional variance of Y given that X = x is Because Y is random, so is ( Y − μ Y.x) 2 and hence ( Y − μ Y.x) 2 has a conditional mean. This can be interpreted as the variance of Y given a sample from the subpopulation where X = x.