How to calculate the variance of prediction results when making predictions

[XingHYu]

Hello, when calculating the variance, should we first denormalize the prediction results and then calculate the variance? In your example, it seems that the variance and mean are calculated first and then denormalized

[piEsposito]

Hello, If we are working with classification, than our output won't be denormalized, as we would use the variance and standard deviation of the probabilities after passing the last layer per a softmax function.

On a regression problem, we could either denormalize it:

And then calculate the variance:

Or calculate the variance qnd then denormalize it by multiplying for the std:

Which would be biased:

.

So, mathematically, the correct is to denormalize and then calculate the variance.

It occurs that, on practice, on regression problems, we may use the variational inference to either calculate confidence intervals (setting bound as some or evaluating the uncertainty by comparing the obtained variance with some . So, if you set your knowing that, using the biased variance may not harm your predictions.

Hope you find my explanation useful.

[piEsposito]

Closing due to inactivity.