some puzzles about the math formulas in the CVAE Future Decoder part

[ultimatedigiman]

As you described in section 3.2 of the paper:

I can understand the purpose of the MSE term ||Y-\hat Y||^2 is to push the real value Y and the mean of the Guassian \hat Y as close as possible,because the Gaussian distribution has the maximum probability value at the mean value. But where did the weighting factor 1/(2beta) come from? Why dividing the variance by beta leads to this weighting factor?

[Khrylx]

This is a typo. It should be 0.5\beta before the MSE term to make it an actual weighting factor. Nice catch

[ultimatedigiman]

This is a typo. It should be 0.5\beta before the MSE term to make it an actual weighting factor. Nice catch

Hi, Could you please figure out why dividing the Guassian standard deviation I by beta leads to the weighting factor 1/(2beta)?

How can I derive the weighting factor 1/(2beta) from the Guassian standard deviation I/beta?

[Khrylx]

Hi,

i already said that it is a typo, it should be 0.5beta ||Y-\hat{Y}||^2.

[ultimatedigiman]

Hi,

i already said that it is a typo, it should be 0.5beta ||Y-\hat{Y}||^2.

Thanks for the quick reply! I'm afraid I mistaken the \beta in your last reply as dividing by beta. But I still don't understand why dividing the Guassian standard deviation I by beta leads to the weighting factor 0.5beta? Is there a derivation process?

[Khrylx]

Hello, sorry for the late reply.

I think if you take the log probability of the GT trajectory Y under the normal distribution, you will get the MSE loss.