Uplift Curves with TMLE Example

This notebook demonstrates the issue of using uplift curves without knowing true treatment effect and how to solve it by using TMLE as a proxy of the true treatment effect.

[2]:

%reload_ext autoreload
%autoreload 2
%matplotlib inline

[3]:

import os
base_path = os.path.abspath("../")
os.chdir(base_path)

[4]:

import logging
from matplotlib import pyplot as plt
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split, KFold
import sys
import warnings
warnings.simplefilter("ignore", UserWarning)

from lightgbm import LGBMRegressor

[5]:

import causalml

from causalml.dataset import synthetic_data
from causalml.inference.meta import BaseXRegressor, TMLELearner
from causalml.metrics.visualize import *
from causalml.propensity import calibrate

import importlib
print(importlib.metadata.version('causalml') )

0.14.0

[8]:

logger = logging.getLogger('causalml')
logger.setLevel(logging.DEBUG)
plt.style.use('fivethirtyeight')

Generating Synthetic Data

[9]:

# Generate synthetic data using mode 1
y, X, treatment, tau, b, e = synthetic_data(mode=1, n=1000000, p=10, sigma=5.)

[10]:

X_train, X_test, y_train, y_test, e_train, e_test, treatment_train, treatment_test, tau_train, tau_test, b_train, b_test = train_test_split(X, y, e, treatment, tau, b, test_size=0.5, random_state=42)

Calculating Individual Treatment Effect (ITE/CATE)

[12]:

# X Learner
learner_x = BaseXRegressor(learner=LGBMRegressor())
learner_x.fit(X=X_train, treatment=treatment_train, y=y_train)
cate_x_test = learner_x.predict(X=X_test, p=e_test, treatment=treatment_test).flatten()

[13]:

alpha=0.2
bins=30
plt.figure(figsize=(12,8))
plt.hist(cate_x_test, alpha=alpha, bins=bins, label='X Learner')
plt.hist(tau_test, alpha=alpha, bins=bins, label='Actual')

plt.title('Distribution of CATE Predictions by X-Learner and Actual')
plt.xlabel('Individual Treatment Effect (ITE/CATE)')
plt.ylabel('# of Samples')
_=plt.legend()

../_images/examples_validation_with_tmle_12_0.png

Validating CATE without TMLE

[14]:

df = pd.DataFrame({'y': y_test, 'w': treatment_test, 'tau': tau_test, 'X-Learner': cate_x_test, 'Actual': tau_test})

Uplift Curve With Ground Truth

If true treatment effect is known as in simulations, the uplift curve of a model uses the cumulative sum of the treatment effect sorted by model’s CATE estimate.

In the figure below, the uplift curve of X-learner shows positive lift close to the optimal lift by the ground truth.

[15]:

plot(df, outcome_col='y', treatment_col='w', treatment_effect_col='tau')

../_images/examples_validation_with_tmle_17_0.png

Uplift Curve Without Ground Truth

If true treatment effect is unknown as in practice, the uplift curve of a model uses the cumulative mean difference of outcome in the treatment and control group sorted by model’s CATE estimate.

In the figure below, the uplift curves of X-learner as well as the ground truth show no lift incorrectly.

[16]:

plot(df.drop('tau', axis=1), outcome_col='y', treatment_col='w')

TMLE

Uplift Curve with TMLE as Ground Truth

By using TMLE as a proxy of the ground truth, the uplift curves of X-learner and the ground truth become close to the original using the ground truth.

[17]:

n_fold = 5
kf = KFold(n_splits=n_fold)

[18]:

df = pd.DataFrame({'y': y_test, 'w': treatment_test, 'p': e_test, 'X-Learner': cate_x_test, 'Actual': tau_test})

[19]:

inference_cols = []
for i in range(X_test.shape[1]):
    col = 'col_' + str(i)
    df[col] = X_test[:,i]
    inference_cols.append(col)

[20]:

df.head()

[20]:

	y	w	p	X-Learner	Actual	col_0	col_1	col_2	col_3	col_4	col_5	col_6	col_7	col_8	col_9
0	6.808806	1	0.750090	0.909261	0.856218	0.911884	0.800551	0.637318	0.584033	0.041204	0.541312	0.183795	0.604942	0.802967	0.321925
1	5.074509	1	0.828351	0.696708	0.613880	0.871032	0.356727	0.168573	0.291071	0.953692	0.838566	0.497353	0.777390	0.811558	0.076717
2	-8.293643	0	0.230920	0.456776	0.335491	0.531401	0.139581	0.604482	0.051055	0.651872	0.878593	0.592694	0.695946	0.972597	0.178291
3	4.511347	0	0.306119	0.189546	0.388202	0.615514	0.160891	0.825520	0.544876	0.107617	0.746920	0.002706	0.963717	0.603323	0.506294
4	5.418169	0	0.293402	0.299151	0.476290	0.839696	0.112883	0.964546	0.336093	0.548355	0.649487	0.905765	0.249261	0.070978	0.947820

[21]:

tmle_df = get_tmlegain(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
                       n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

[22]:

tmle_df

[22]:

	X-Learner	Actual	Random
0.0	0.000000	0.000000	0.000000
0.2	0.137463	0.150106	0.095493
0.4	0.254839	0.267014	0.190986
0.6	0.346940	0.359990	0.286479
0.8	0.434913	0.447867	0.381972
1.0	0.477465	0.477465	0.477465

Uplift Curve wihtout CI

Here we can directly use plot_tmle() function to generate the results and plot uplift curve

[23]:

plot_tmlegain(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
              n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

../_images/examples_validation_with_tmle_32_0.png

We also provide the api call directly with plot() by input the kind as 'tmle'

[24]:

plot(df, kind='gain', tmle=True, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
     n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

../_images/examples_validation_with_tmle_34_0.png

AUUC Score

[25]:

auuc_score(df, tmle=True, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
           n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

[25]:

X-Learner    0.275270
Actual       0.283740
Random       0.238733
dtype: float64

Uplift Curve with CI

[25]:

tmle_df = get_tmlegain(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
                       n_segment=5, cv=kf, calibrate_propensity=True, ci=True)

[26]:

tmle_df

[26]:

	X-Learner	Actual	X-Learner LB	Actual LB	X-Learner UB	Actual UB	Random
0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
0.2	0.145151	0.146628	0.127016	0.127210	0.163285	0.166046	0.096077
0.4	0.252563	0.255667	0.216629	0.218323	0.288496	0.293011	0.192154
0.6	0.352174	0.364541	0.300866	0.313233	0.403483	0.415850	0.288231
0.8	0.433351	0.446890	0.366285	0.380624	0.500417	0.513157	0.384308
1.0	0.480384	0.480384	0.441999	0.441999	0.518770	0.518770	0.480384

[27]:

plot_tmlegain(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
              n_segment=5, cv=kf, calibrate_propensity=True, ci=True)

../_images/examples_validation_with_tmle_40_0.png

[29]:

plot(df, kind='gain', tmle=True, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
     n_segment=5, cv=kf, calibrate_propensity=True, ci=True)

../_images/examples_validation_with_tmle_41_0.png

Qini Curve with TMLE as Ground Truth

Qini Curve without CI

[30]:

qini = get_tmleqini(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
                    n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

[31]:

qini

[31]:

	X-Learner	Actual	Random
0.0	0.000000	0.000000	0.000000
100000.0	53513.373815	59840.329296	24964.329463
200000.0	92693.576894	104578.508000	49928.658925
300000.0	121232.782373	132653.427128	74892.988388
400000.0	136045.083604	145388.277994	99857.317851
500000.0	124821.647313	124821.647313	124821.647313

[32]:

plot_tmleqini(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
              n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

../_images/examples_validation_with_tmle_46_0.png

We also provide the api call directly with plot() by input the kind as 'tmleqini'

[34]:

plot(df, kind='qini', tmle=True, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
     n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

../_images/examples_validation_with_tmle_48_0.png

Qini Score

[26]:

qini_score(df, tmle=True, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
           n_segment=5, cv=kf, calibrate_propensity=True, ci=False)

[26]:

X-Learner    23814.998608
Actual       33683.500462
Random           0.000000
dtype: float64

Qini Curve with CI

[36]:

qini = get_tmleqini(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
                    n_segment=5, cv=kf, calibrate_propensity=True, ci=True)

[37]:

qini

[37]:

	X-Learner	Actual	X-Learner LB	Actual LB	X-Learner UB	Actual UB	Random
0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
100000.0	53513.373815	59840.329296	46827.611036	51915.622165	60199.136594	67765.036427	24964.329463
200000.0	92693.576894	104578.508000	79515.426034	89298.783725	105871.727753	119858.232275	49928.658925
300000.0	121232.782373	132653.427128	103649.630931	113772.913012	138815.933816	151533.941243	74892.988388
400000.0	136045.083604	145388.277994	115586.643138	124194.530581	156503.524070	166582.025407	99857.317851
500000.0	124821.647313	124821.647313	124821.647313	124821.647313	124821.647313	124821.647313	124821.647313

[38]:

plot_tmleqini(df, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
              n_segment=5, cv=kf, calibrate_propensity=True, ci=True)

../_images/examples_validation_with_tmle_54_0.png

[39]:

plot(df, kind='qini', tmle=True, inference_col=inference_cols, outcome_col='y', treatment_col='w', p_col='p',
     n_segment=5, cv=kf, calibrate_propensity=True, ci=True)

../_images/examples_validation_with_tmle_55_0.png