What is a Qini Curve 🌱
The Qini Curve is the Cumulative ITE on the treated
- The area is the area between this curve and the random uplift curve which is just a straight line from (0,0) to the rightmost point of your Qini Curve \(\text { Qini Curve Area }=\sum_{i=0}^{M-1} \frac{1}{2}\left(\frac{n_{t, y=1}\left(\phi_{i+1}\right)-n_{t, y=1}\left(\phi_{i}\right)}{N_{t}}-\frac{n_{c, y=1}\left(\phi_{i+1}\right)-n_{c, y=1}\left(\phi_{i}\right)}{N_{c}}\right) \frac{1}{M}\)
where $\phi_i = i/M$.
\[\text { Qini Curve Area }=\sum_{i=0}^{M-1} \frac{1}{2}\left(\operatorname{Qini} \operatorname{curve}\left(\phi_{i+1}\right)+\operatorname{Qini} \operatorname{curve}\left(\phi_{i}\right)\right)\left(\phi_{i+1}-\phi_{i}\right)\] \[\text { Randomized Qini Area }= \frac{1}{2}(\operatorname{Qini} \operatorname{curve}(\phi_{M}))\] \[Q = \text { Qini Curve Area } - \text { Randomized Qini Area }\] \[f(t)=\left(\frac{Y_{t}^{T}}{N_{t}^{T}}-\frac{Y_{t}^{C}}{N_{t}^{C}}\right)\left(N_{t}^{T}+N_{t}^{C}\right)\] \[g(t)=Y_{t}^{T}-\frac{Y_{t}^{C} N_{t}^{T}}{N_{t}^{C}}\]for the $t$ datapoints sorted by largest predicted ITE/Uplift, We calculate
- I think it is just cumulative ITE in order of decreasing predicted ITEs
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