For the harmonic mean, the partial derivative for either P or R is going to be bounded between 0 and 2. But for the geometric mean, the partial derivative would be sqrt(R/P)/2 wrt to P and sqrt(P/R)/2 wrt to R, and these partial derivatives can easily blow up to inf when the denominator becomes very small and may not be good for learning, and thus the harmonic mean is better. Just my thoughts 🤪
On your final question: Geometric mean would skew toward higher scores in general when compared to the harmonic mean, therefore less informative than the harmonic mean?
The idea of diminishing returns - we can also get it with idea 1 by looking at the percentage change in the score, and not looking at the score in absolute terms.
I tried with the geometric mean (derivating it, plotting it, ...) and did the same analysis as 10:51, the technique ticked all the requirements. So I'm left wondering, why don't we use it more often ? (Nice video !)
If you look at the harmonic mean based in the true and false positives and negatives it does not seems so complicated: Tp: True positives Fp: False positives Fn: False negatives Precision: Tp/(tp+fp) Recall: Tp/(tp+fn) Sum: (tp(tp+fn)+tp(tp+fp)) / (tp+fp)(tp+fn) (tp(2tp+fn+fp))/(tp+fp)(tp+fn) Multiplication: tp²/(tp+fp)(tp+fn) Harmonic mean: (tp²/(tp+fp)(tp+fn)) / ((tp(2tp+fn+fp))/((tp+fp)(tp+fn))) Tp/(2tp+fn+tp)
For GM the partial derivative w.r.t precision would be (R/sqrt(R*P)), similarly for recall. It also plays same role of reducing the gradient, if you could comment, why it is not used ?
! James 1:17 LSB - Every good thing given and every perfect gift is from above, coming down from the Father of lights, with whom there is no variation or shifting shadow.
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I still can't believe that I found a video that solved my specific doubts on F1-score with such a brilliant approach. Thanks for the effort!
Best explanation I've ever seen about F1
For the harmonic mean, the partial derivative for either P or R is going to be bounded between 0 and 2. But for the geometric mean, the partial derivative would be sqrt(R/P)/2 wrt to P and sqrt(P/R)/2 wrt to R, and these partial derivatives can easily blow up to inf when the denominator becomes very small and may not be good for learning, and thus the harmonic mean is better. Just my thoughts 🤪
On your final question: Geometric mean would skew toward higher scores in general when compared to the harmonic mean, therefore less informative than the harmonic mean?
The idea of diminishing returns - we can also get it with idea 1 by looking at the percentage change in the score, and not looking at the score in absolute terms.
I tried with the geometric mean (derivating it, plotting it, ...) and did the same analysis as 10:51, the technique ticked all the requirements. So I'm left wondering, why don't we use it more often ?
(Nice video !)
If you look at the harmonic mean based in the true and false positives and negatives it does not seems so complicated:
Tp: True positives
Fp: False positives
Fn: False negatives
Precision:
Tp/(tp+fp)
Recall:
Tp/(tp+fn)
Sum:
(tp(tp+fn)+tp(tp+fp))
/
(tp+fp)(tp+fn)
(tp(2tp+fn+fp))/(tp+fp)(tp+fn)
Multiplication:
tp²/(tp+fp)(tp+fn)
Harmonic mean:
(tp²/(tp+fp)(tp+fn))
/
((tp(2tp+fn+fp))/((tp+fp)(tp+fn)))
Tp/(2tp+fn+tp)
Really like your explanation! thank you!
For GM the partial derivative w.r.t precision would be (R/sqrt(R*P)), similarly for recall.
It also plays same role of reducing the gradient, if you could comment, why it is not used ?
It's just harmonic mean
Well, duh
I see some middle eastern humor in your teaching style!
Don't take them as gifts from god!
Reminds me the joke of Isaac Newton under the apple 🍎 tree
! James 1:17 LSB - Every good thing given and every perfect gift is from above, coming down from the Father of lights, with whom there is no variation or shifting shadow.