What is a Qini Curve 🌱

Last updated on March 13, 2021

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 $Qini Curve Area = \sum_{i = 0}^{M - 1} \frac{1}{2} (\frac{n_{t, y = 1} (ϕ_{i + 1}) - n_{t, y = 1} (ϕ_{i})}{N_{t}} - \frac{n_{c, y = 1} (ϕ_{i + 1}) - n_{c, y = 1} (ϕ_{i})}{N_{c}}) \frac{1}{M}$

where $ϕ_{i} = i / M$ .

Qini Curve Area = \sum_{i = 0}^{M - 1} \frac{1}{2} (Qini curve (ϕ_{i + 1}) + Qini curve (ϕ_{i})) (ϕ_{i + 1} - ϕ_{i})

Randomized Qini Area = \frac{1}{2} (Qini curve (ϕ_{M}))

Q = Qini Curve Area - Randomized Qini Area

f (t) = (\frac{Y_{t}^{T}}{N_{t}^{T}} - \frac{Y_{t}^{C}}{N_{t}^{C}}) (N_{t}^{T} + N_{t}^{C})

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

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