🔗 Qini Coefficient

Qini Coefficient#

A normalised summary of the Qini curve measuring uplift-model performance.

Important

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What it is#

The Qini coefficient is a single-number performance metric for uplift models — their equivalent of AUC. Where AUC asks how well a classifier predicts who will buy, the Qini coefficient asks how well an uplift model ranks people by who will buy because of the treatment.

How it’s computed#

Sort customers by predicted uplift (descending), split them into deciles or percentiles, and plot the Qini curve — cumulative incremental response (treatment minus control) against the proportion targeted. The coefficient is the normalised area between the model’s curve and the random-targeting diagonal.

The formula#

\[\text{Qini} = \frac{\int_0^1 \left( G_{\text{model}}(x) - G_{\text{random}}(x) \right) dx}{\int_0^1 \left( G_{\text{perfect}}(x) - G_{\text{random}}(x) \right) dx}.\]

It ranges from 0 to 1 — 0.5 and up is decent, and close to 1 is excellent separation.

A worked example, and cousins#

Targeting the top 20%, a random selection might yield +100 purchases while the model yields +300 — the model curve sits above random, and the coefficient quantifies that gap. It is the normalised form of the AUUC (raw area under the uplift curve), which makes it comparable across datasets: ROC-AUC is to classification what the Qini coefficient is to uplift.

Theme: Causal Inference & Uplift · All terminology

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Mind map — connected ideas

Qini Curve · Uplift Score · AUUC (Area Under the Uplift Curve) · Uplift Models · Cumulative Incremental Gain (CIG) · Total Incremental Benefit (TIB)

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More in Causal Inference & Uplift

AUUC (Area Under the Uplift Curve) · Causal Effect · Causal Impact · Causal Inference · Causal ML (Causal Machine Learning) · Causal Trees · Cumulative Incremental Gain (CIG) · Cumulative Uplift · Incremental Conversions · Incremental Gain · Incremental Recovery Rate (IRR) · Incremental Revenue · Incremental Sales · Qini Curve