Conformal risk control question about conformal-prediction HOT 5 CLOSED

from conformal-prediction.

Hi, thank you so much for the great work. I have a question regarding the notebook on conformal risk control.

in the notebook, you defined the risk optimization objective as

def lamhat_threshold(lam): return false_negative_rate(cal_sgmd>=lam, cal_gt_masks) - ((n+1)/n*alpha - 1/(n+1))

However, in section 4.3 of the paper, it is defined as α−B−αn, which means the denominator should be n. Why is it n+1 in the code? Thanks.

n is large, e.g. n = 500, so 1/(n+1) ≈ 1/n ?

from conformal-prediction.

Ah - sorry, don't want to leave this unfinished. Actually, it should be true with equality, and I think you may have caught a bug. Here's the derivation:

(n+1)/n*alpha - 1/n
= alpha + (1/n)alpha - 1/n
= alpha - ((1-alpha)/n)

So, you're right! Thanks so much!

Maybe you should make a PR? That way you'll get some credit 😀

Otherwise if I don't hear from you, I'll just fix it myself soon. Thanks so much again!!

from conformal-prediction.

Ah - sorry, don't want to leave this unfinished. Actually, it should be true with equality, and I think you may have caught a bug. Here's the derivation:

(n+1)/n*alpha - 1/n = alpha + (1/n)alpha - 1/n = alpha - ((1-alpha)/n)

So, you're right! Thanks so much!

Maybe you should make a PR? That way you'll get some credit 😀

Otherwise if I don't hear from you, I'll just fix it myself soon. Thanks so much again!!

Thanks Anastasios, but I think you made a typo, the derivation should start from (n+1)/n*alpha - 1/(n+1), as shown in code

from conformal-prediction.

I was proving that the code is wrong! 😀

It should be what I said in my message. The expression I started with is the correct version.

from conformal-prediction.