Calculate individual class probabilities

[HareeshBahuleyan]

Thanks for sharing this useful library. The instructions on the documentation page are clear and easy to follow.

My question is regarding the output probabilities. As I understand, both coral and corn outputs cumulative probabilities. For instance, if we are dealing with a 5-class (classes 0 to 4) problem, then the 4 probabilities output are:

[p(y > 0), p(y > 1), p(y > 2), p(y > 3)]

Is there a way to obtain individual class probabilities from this, such as p(y=1), p(y=2) and so on?

Would you say the following is valid to do?

P(0) = 1 - P(y>0) 
P(1) = P(y>0) - P(y>1)
P(2) = P(y>1) - P(y>2)
P(3) = P(y>2) - P(y>3)
P(4) = P(y>3)

[rasbt]

Yes, this should be valid.

[HareeshBahuleyan]

Thanks @rasbt for the reply.

For my use case when I applied this, there seemed to be a mismatch between the label calculated via argmax over the individual probabilities obtained using the above formulae vs. the predicted label obtained via proba_to_label.

Here is an example:

Method 1: Using argmax over individual probabilities

p(y>0)	0.72
p(y>1)	0.55
p(y>2)	0.32
p(y>3)	0.25

p(y=0)	0.28
p(y=1)	0.17
p(y=2)	0.23
p(y=3)	0.07
p(y=4)	0.25
---
p(total) 1.0

index of predicted class via argmax -> 0

Method 2: Using proba_to_label

probas = [0.72, 0.55, 0.32, 0.25]
predict_levels = probas > 0.5 # [1, 1, 0, 0]
predicted_labels = torch.sum(predict_levels, dim=1) # 2

index of predicted class via proba_to_label -> 2

Is there some that I might be missing here? Or do you know why this discrepancy occurs?

[rasbt]

That's a good point. Both are slightly different ways for obtaining the final label and they don't have to necessarily produce the same label all the time. E.g., it could be that you have something like [0.6, 0.5, 0.4, 0.1]. In this case the approach we use in the paper yields label 3 because of sum([1, 1, 0, 0])+1) and via argmax on

P(0) = 1 - P(y>0) = 0.4
P(1) = P(y>0) - P(y>1) = 0.1
P(2) = P(y>1) - P(y>2) = 0.1
P(3) = P(y>2) - P(y>3) = 0.3

you'd get label 0.

[HareeshBahuleyan]

Understood, thanks for the clarification.