another question about p_hat

[ShellingFord221]

Why do you only use [0] of prediction results in line 63, /retina/utils.py? Shouldn't p_hat be made up of the probabilities of all classes?

[ShellingFord221]

In your paper, the explanation of p_hat under Eq. 4 is: p_hat = Softmax{f(x*)}, therefore I think that p_hat should be made up of the probabilities of all classes after softmax layer.

[ykwon0407]

@ShellingFord221 Hello~ Why do you only use [0] of prediction results in line 63, /retina/utils.py? Shouldn't p_hat be made up of the probabilities of all classes? In your paper, the explanation of p_hat under Eq. 4 is: p_hat = Softmax{f(x*)}, therefore I think that p_hat should be made up of the probabilities of all classes after softmax layer. -> You are right. However, in this GitHub codes, the similar concept applied to another issue you wrote goes again, indexing [0] is enough to obtain the p_hat. Please note that knowing P(y=1) is sufficient to know p_hat in case of binary classification.

Hope this information helps you!

[ShellingFord221]

Hi, I suddenly realize that p_hat is just for ONE test data according to the explanation under Eq. 4: p_hat = Softmax{f(x)}, where x means a new input. Can I rewrite Eq. 4 to get aleatoric and epistemic uncertainty of ALL test data (e.g. 10000 samples)? Because I think the uncertainty metrics are more appropriate in the case of all test data, aleatoric and epistemic uncertainty should mean the uncertainty about the whole test set.

[ykwon0407]

Not really. It is because, in general, the 'uncertainty' is terminology for one random variable X. Once you have averaged the uncertainties using whole test data, then it would estimate Var(y), not Var(y | x).

If you want to see overall uncertainty, then I guess you can compute by averaging all terms. It depends on what quantity you want.