lift-area-ratio 0.1.1

Lift Area Ratio — a population-independent model discrimination metric

LAR — Lift Area Ratio

A population-independent metric for binary classification model discrimination, designed as a more interpretable alternative to ROC-AUC.

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Why not just use AUC?

AUC averages performance across all thresholds equally — including thresholds you'll never use in production. Two models can have the same AUC but behave very differently at your actual operating point.

LAR answers a more practical question:

"How much better than random is my model at concentrating positives at the top of the ranking?"

And unlike AUC, LAR is population independent — it gives comparable scores across datasets with different event rates.

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How it works

LAR is based on the Event Rate Ratio (ERR) — at a given percentile, how much more concentrated are positives compared to the overall population:

$$ERR = \frac{b/n}{B/N}$$

Where:

• N = total observations, B = total positives
• n = observations up to percentile, b = positives found up to percentile

Plotting ERR across all percentiles gives three reference curves:

• 🔵 Oracle — perfect model, all positives ranked first. ERR starts at N/B and drops sharply once all positives are found
• ⚫ Your model — sits between oracle and random
• 🔴 Random — flat line at ERR = 1, no discrimination

LAR is the ratio of the areas above the random line:

$$LAR = \frac{A}{O} = \frac{\text{area under model curve}}{\text{area under oracle curve}}$$

LAR value	Meaning
0	model has no skill (= random)
1	perfect model (= oracle)
0.83	model captures 83% of perfect discrimination

Since both areas are scaled by the same oracle, the population event rate cancels out — making LAR directly comparable across different datasets and models.

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Installation

pip install lar

Or install from source:

git clone https://github.com/yourname/lar.git
cd lar
pip install -e .

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Quick start

import numpy as np
from lar import LiftAreaRatio

# your model scores and true labels
scores = model.predict_proba(X)[:, 1]
y = df["default_flag"]

# compute LAR
lar = LiftAreaRatio(n_percentiles=100)
result = lar.fit(scores, y)

# print summary
lar.summary(result)
# =============================================
#   Lift Area Ratio — Summary
# =============================================
#   N (observations) : 2000
#   B (positives)    : 197
#   Event rate (ER)  : 9.85%
#   Max ERR (oracle) : 10.15
# ---------------------------------------------
#   Area model       : 192.66
#   Area oracle      : 231.72
#   LAR  = A / O     : 0.8314
# ---------------------------------------------
#   Interpretation   : model achieves 83.1% of perfect discrimination
# =============================================

# plot lift curves
lar.plot(result, title="My Model")

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API

LiftAreaRatio(n_percentiles=100)

Parameter	Type	Default	Description
n_percentiles	int	100	number of quantile bins

.fit(scores, y) → LARResult

Parameter	Type	Description
scores	array-like	model risk scores (higher = more likely positive)
y	array-like	binary labels (1 = positive, 0 = negative)

.summary(result)

Prints a formatted summary of the LAR result.

.plot(result, title, figsize)

Plots oracle, model and random lift curves with shaded areas A and O.

LARResult fields

Field	Description
lar	final LAR score
area_model	area under model lift curve
area_oracle	area under oracle lift curve
N	total observations
B	total positives
event_rate	B / N
lift_model	DataFrame with percentile and ERR per bin
lift_oracle	DataFrame with percentile and ERR for oracle

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Requirements

• Python >= 3.8
• numpy
• pandas
• matplotlib