import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
matplotlib.RcParams._get = dict.get
IV (Instrument Variable)#
문제 정의#
import numpy as np
import pandas as pd
import lightgbm as lgb
from econml.iv.dr import LinearIntentToTreatDRIV
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression, LogisticRegression
import matplotlib.pyplot as plt
%matplotlib inline
file_url = "https://raw.githubusercontent.com/py-why/EconML/refs/heads/data/datasets/RecommendationAB/ab_sample.csv"
ab_data = pd.read_csv(file_url)
ab_data.head()
| days_visited_exp_pre | days_visited_free_pre | days_visited_fs_pre | days_visited_hs_pre | days_visited_rs_pre | days_visited_vrs_pre | locale_en_US | revenue_pre | os_type_osx | os_type_windows | easier_signup | became_member | days_visited_post | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 9 | 7 | 25 | 6 | 3 | 1 | 0.01 | 0 | 1 | 0 | 0 | 1 |
| 1 | 10 | 25 | 27 | 10 | 27 | 27 | 0 | 2.26 | 0 | 0 | 0 | 0 | 15 |
| 2 | 18 | 14 | 8 | 4 | 5 | 2 | 1 | 0.03 | 0 | 1 | 0 | 0 | 17 |
| 3 | 17 | 0 | 23 | 2 | 3 | 1 | 1 | 418.77 | 0 | 1 | 0 | 0 | 6 |
| 4 | 24 | 9 | 22 | 2 | 3 | 18 | 1 | 1.54 | 0 | 0 | 0 | 0 | 12 |
Z = ab_data['easier_signup'] # nudge, or instrument
T = ab_data['became_member'] # intervention, or treatment
Y = ab_data['days_visited_post'] # outcome of interest
X_data = ab_data.drop(columns=['easier_signup', 'became_member', 'days_visited_post']) # features
from graphviz import Digraph
dot = Digraph(comment='Instrumental Variable DAG')
# Nodes
dot.node('Z', 'Z: easier_signup\n(Instrument)')
dot.node('T', 'T: became_member\n(Treatment)')
dot.node('Y', 'Y: days_visited_post\n(Outcome)')
dot.node('X', 'X: user pre-features\n(confounders)')
# Edges
dot.edge('Z', 'T', label='relevance')
dot.edge('T', 'Y', label='causal effect')
dot.edge('X', 'T')
dot.edge('X', 'Y')
# Exclusion restriction (optional, dashed)
dot.edge('Z', 'Y', style='dashed', label='no direct effect')
dot
가정 체크#
Relevance: signup을 해야지만, member가 될 수 있기 때문에 Z는 효과적인 도구변수이다. 이를 현실적으로 수치로도 확인해볼 수 있다.
Independence: easier_signup은 A/B 실험으로 무작위 배정된 UI 변경이기에 잠재 변수들과 독립일 가능성이 높다.
Exclusion Restriction (No Direct Effect): UI 변경이 방문일수를 직접적으로 바꾸지는 않는다.
Monotonicity: signup을 쉽게 만들었는데 오히려 회원가입을 포기할 사람은 거의 없을 것이다.
# Relevance
print("P(T=1|Z=1) =", T[Z==1].mean())
print("P(T=1|Z=0) =", T[Z==0].mean())
print("Diff =", T[Z==1].mean() - T[Z==0].mean())
P(T=1|Z=1) = 0.6978538028056432
P(T=1|Z=0) = 0.005965010608911485
Diff = 0.6918887921967317
Modeling#
Wald Estimate#
Linear Regression을 통해 추정 가능하다:
\[ \theta \;:=\; \frac{ \mathbb{E}_{X}\!\left[ \mathbb{E}\!\left[\,Y \mid Z=1, X\,\right] - \mathbb{E}\!\left[\,Y \mid Z=0, X\,\right] \right] }{ \mathbb{E}_{X}\!\left[ \mathbb{E}\!\left[\,T \mid Z=1, X\,\right] - \mathbb{E}\!\left[\,T \mid Z=0, X\,\right] \right] }. \]
XZ = pd.concat([Z, X_data], axis=1)
model_y = LinearRegression()
model_y.fit(XZ, Y)
model_t = LogisticRegression(
solver="liblinear",
max_iter=5000
)
model_t.fit(XZ, T)
XZ_1 = XZ.copy()
XZ_1['easier_signup'] = 1
XZ_0 = XZ.copy()
XZ_0['easier_signup'] = 0
num = np.mean(model_y.predict(XZ_1) - model_y.predict(XZ_0))
den = np.mean(
model_t.predict_proba(XZ_1)[:, 1]
- model_t.predict_proba(XZ_0)[:, 1]
)
theta = num / den
theta
np.float64(2.4303712760282243)
LinearIntentToTreatDRIV#
식을 DoublyRobust하게 뽑을 수 있으며, ML도 결합하여 사용할 수 있다.
lgb_T_XZ_params = {
'objective' : 'binary',
'metric' : 'auc',
'learning_rate': 0.1,
'num_leaves' : 30,
'max_depth' : 5
}
lgb_Y_X_params = {
'metric' : 'rmse',
'learning_rate': 0.1,
'num_leaves' : 30,
'max_depth' : 5
}
model_T_XZ = lgb.LGBMClassifier(**lgb_T_XZ_params)
model_Y_X = lgb.LGBMRegressor(**lgb_Y_X_params)
flexible_model_effect = lgb.LGBMRegressor(**lgb_Y_X_params)
model = LinearIntentToTreatDRIV(
model_y_xw = model_Y_X,
model_t_xwz = model_T_XZ,
flexible_model_effect = flexible_model_effect,
featurizer = PolynomialFeatures(degree=1, include_bias=False)
)
model.fit(Y, T, Z=Z, X=X_data, inference="statsmodels")
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000962 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 100000, number of used features: 10
[LightGBM] [Info] Start training from score 9.952170
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Info] Number of positive: 35220, number of negative: 64780
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000952 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 100000, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352200 -> initscore=-0.609383
[LightGBM] [Info] Start training from score -0.609383
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000775 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 100000, number of used features: 10
[LightGBM] [Info] Start training from score 2.718645
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000535 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66666, number of used features: 10
[LightGBM] [Info] Start training from score 9.937464
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Number of positive: 23480, number of negative: 43186
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000625 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 66666, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352204 -> initscore=-0.609367
[LightGBM] [Info] Start training from score -0.609367
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000580 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66666, number of used features: 10
[LightGBM] [Info] Start training from score 9.937464
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Info] Number of positive: 23480, number of negative: 43186
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000666 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 66666, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352204 -> initscore=-0.609367
[LightGBM] [Info] Start training from score -0.609367
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.001835 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66666, number of used features: 10
[LightGBM] [Info] Start training from score 2.721393
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000636 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 10
[LightGBM] [Info] Start training from score 9.979345
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Number of positive: 23480, number of negative: 43187
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000615 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352198 -> initscore=-0.609391
[LightGBM] [Info] Start training from score -0.609391
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
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[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000954 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 10
[LightGBM] [Info] Start training from score 9.979345
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Number of positive: 23480, number of negative: 43187
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000585 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352198 -> initscore=-0.609391
[LightGBM] [Info] Start training from score -0.609391
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000504 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 10
[LightGBM] [Info] Start training from score 2.711452
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000736 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 10
[LightGBM] [Info] Start training from score 9.939700
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Number of positive: 23480, number of negative: 43187
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000474 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352198 -> initscore=-0.609391
[LightGBM] [Info] Start training from score -0.609391
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000623 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 10
[LightGBM] [Info] Start training from score 9.939700
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Info] Number of positive: 23480, number of negative: 43187
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000563 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 437
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 11
[LightGBM] [Info] [binary:BoostFromScore]: pavg=0.352198 -> initscore=-0.609391
[LightGBM] [Info] Start training from score -0.609391
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000819 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 435
[LightGBM] [Info] Number of data points in the train set: 66667, number of used features: 10
[LightGBM] [Info] Start training from score 2.706137
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
[LightGBM] [Warning] No further splits with positive gain, best gain: -inf
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMClassifier was fitted with feature names
warnings.warn(
/Users/jhkim/miniconda3/envs/scpi-env/lib/python3.11/site-packages/sklearn/utils/validation.py:2739: UserWarning: X does not have valid feature names, but LGBMRegressor was fitted with feature names
warnings.warn(
<econml.iv.dr._dr.LinearIntentToTreatDRIV at 0x189521b50>
late = model.ate(X=X_data)
late_ci = model.ate_interval(X=X_data)
print("IV-based mean effect (LATE avg over X):", late)
print("CI:", late_ci)
IV-based mean effect (LATE avg over X): 2.0445852355071112
CI: (np.float64(1.9336189424389112), np.float64(2.1555515285753115))
CATE#
coef_indices = np.arange(model.coef_.shape[0])
coef_error = np.asarray(model.coef__interval())
coef_error[0, :] = model.coef_ - coef_error[0, :]
coef_error[1, :] = coef_error[1, :] - model.coef_
plt.errorbar(coef_indices, model.coef_, coef_error, fmt="o", label="Learned coefficients\nand 95% confidence interval")
plt.xticks(coef_indices, X_data.columns, rotation='vertical')
plt.legend()
plt.show()
model.summary()
| point_estimate | stderr | zstat | pvalue | ci_lower | ci_upper | |
|---|---|---|---|---|---|---|
| days_visited_exp_pre | 0.001 | 0.007 | 0.162 | 0.871 | -0.012 | 0.014 |
| days_visited_free_pre | 0.285 | 0.007 | 38.287 | 0.0 | 0.27 | 0.299 |
| days_visited_fs_pre | -0.008 | 0.007 | -1.165 | 0.244 | -0.021 | 0.005 |
| days_visited_hs_pre | -0.19 | 0.007 | -28.112 | 0.0 | -0.203 | -0.177 |
| days_visited_rs_pre | 0.001 | 0.007 | 0.112 | 0.91 | -0.012 | 0.014 |
| days_visited_vrs_pre | -0.001 | 0.007 | -0.211 | 0.833 | -0.015 | 0.012 |
| locale_en_US | -0.034 | 0.113 | -0.303 | 0.762 | -0.256 | 0.188 |
| revenue_pre | -0.0 | 0.0 | -0.926 | 0.354 | -0.0 | 0.0 |
| os_type_osx | 0.935 | 0.139 | 6.731 | 0.0 | 0.662 | 1.207 |
| os_type_windows | 0.021 | 0.138 | 0.15 | 0.881 | -0.251 | 0.292 |
| point_estimate | stderr | zstat | pvalue | ci_lower | ci_upper | |
|---|---|---|---|---|---|---|
| cate_intercept | 0.523 | 0.27 | 1.937 | 0.053 | -0.006 | 1.052 |
A linear parametric conditional average treatment effect (CATE) model was fitted:
$Y = \Theta(X)\cdot T + g(X, W) + \epsilon$
where for every outcome $i$ and treatment $j$ the CATE $\Theta_{ij}(X)$ has the form:
$\Theta_{ij}(X) = \phi(X)' coef_{ij} + cate\_intercept_{ij}$
where $\phi(X)$ is the output of the `featurizer`
Coefficient Results table portrays the $coef_{ij}$ parameter vector for each outcome $i$ and treatment $j$. Intercept Results table portrays the $cate\_intercept_{ij}$ parameter.
각 계수의 해석이 가능하다: “이 변수가 1만큼 증가하면, ‘회원이 되었을 때의 효과’가 얼마나 변하는가?”
e.g. days_visited_free_pre = +0.285 (매우 유의) -> free 콘텐츠를 많₩이 쓰던 유저일수록 회원가입 채널을 쉽게 바꿨을때의 효과가 크게 증가