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Heterogeneous Treatment Effect (HTE) estimation using EconML.
We estimate the Conditional Average Treatment Effect (CATE):
Ο(x) = E[Y(1) - Y(0) | X = x]
Three estimators are compared:
1. T-Learner β separate outcome models per arm; simple but high variance
2. X-Learner β cross-fitted residuals; better for imbalanced arms
3. CausalForestDML β doubly-robust DML + causal forest; SOTA for HTE
Reference for CausalForestDML: Athey, Tibshirani, Wager (2019)
"Generalized Random Forests." Annals of Statistics.
"""
from __future__ import annotations
import json
import numpy as np
import pandas as pd
from pathlib import Path
from typing import Optional
FEATURE_COLS = ["recency", "history", "mens", "womens", "newbie",
"zip_urban", "zip_suburban", "zip_rural",
"channel_web", "channel_phone", "channel_multichannel"]
def prepare_hillstrom(df: pd.DataFrame) -> pd.DataFrame:
"""
Clean and encode the Hillstrom dataset for HTE estimation.
Binary treatment: 0 = No E-Mail, 1 = any e-mail (Men's or Women's)
Outcome: conversion (binary), spend (continuous)
"""
df = df.copy()
df.columns = df.columns.str.lower().str.strip()
# Binary treatment
df["treatment"] = (df["segment"] != "No E-Mail").astype(int)
# One-hot encode zip_code and channel
df["zip_urban"] = (df["zip_code"] == "Urban").astype(int)
df["zip_suburban"] = (df["zip_code"] == "Surban").astype(int)
df["zip_rural"] = (df["zip_code"] == "Rural").astype(int)
df["channel_web"] = (df["channel"] == "Web").astype(int)
df["channel_phone"] = (df["channel"] == "Phone").astype(int)
df["channel_multichannel"] = (df["channel"] == "Multichannel").astype(int)
# Rename outcome columns for clarity
df.rename(columns={"conversion": "conversion", "spend": "spend"}, inplace=True)
# Log-transform history to reduce skew
df["history"] = np.log1p(df["history"])
return df
def run_hte_analysis(
df: pd.DataFrame,
outcome_col: str = "conversion",
n_estimators: int = 200,
seed: int = 42,
) -> dict:
"""
Run all three HTE estimators and return a summary dict.
Returns CATE estimates per user plus segment-level aggregations.
"""
try:
from econml.metalearners import TLearner, XLearner
from econml.dml import CausalForestDML
from sklearn.ensemble import GradientBoostingClassifier, GradientBoostingRegressor
from sklearn.linear_model import LogisticRegression
from sklearn.preprocessing import StandardScaler
except ImportError as e:
raise ImportError(f"Install econml and scikit-learn: {e}")
df_clean = prepare_hillstrom(df)
available_feats = [c for c in FEATURE_COLS if c in df_clean.columns]
X = df_clean[available_feats].values.astype(float)
T = df_clean["treatment"].values.astype(float)
Y = df_clean[outcome_col].values.astype(float)
results: dict[str, np.ndarray] = {}
# ββ T-Learner βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
# Each learner gets its OWN model instance β sharing causes cross-contamination.
def _make_base():
if outcome_col == "conversion":
return GradientBoostingClassifier(n_estimators=n_estimators,
max_depth=4, random_state=seed)
return GradientBoostingRegressor(n_estimators=n_estimators,
max_depth=4, random_state=seed)
t_learner = TLearner(models=_make_base())
t_learner.fit(Y, T, X=X)
results["T-Learner"] = t_learner.effect(X).flatten()
# ββ X-Learner βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
x_learner = XLearner(models=_make_base())
x_learner.fit(Y, T, X=X)
results["X-Learner"] = x_learner.effect(X).flatten()
# ββ CausalForestDML (SOTA) ββββββββββββββββββββββββββββββββββββββββββββββββ
# DML residualises both Y and T using regressors:
# - model_y: fits E[Y|X] (conditional outcome, treated as continuous)
# - model_t: fits E[T|X] (propensity score, treated as continuous β [0,1])
# Using regressors for both avoids DML's classifier-rejection check.
model_y_cf = GradientBoostingRegressor(n_estimators=100, random_state=seed)
model_t_cf = GradientBoostingRegressor(n_estimators=100, random_state=seed,
loss='squared_error')
cf = CausalForestDML(
model_y=model_y_cf,
model_t=model_t_cf,
n_estimators=n_estimators,
random_state=seed,
verbose=0,
)
cf.fit(Y, T, X=X)
cate_cf = cf.effect(X)
cate_lb, cate_ub = cf.effect_interval(X)
results["CausalForest"] = cate_cf.flatten()
results["CausalForest_lb"] = cate_lb.flatten()
results["CausalForest_ub"] = cate_ub.flatten()
# ββ Build output DataFrame ββββββββββββββββββββββββββββββββββββββββββββββββ
cate_df = df_clean[available_feats + ["treatment", outcome_col]].copy()
cate_df["segment_email"] = df["segment"] if "segment" in df.columns else df_clean["treatment"].map({0: "No E-Mail", 1: "E-Mail"})
for name, vals in results.items():
cate_df[f"cate_{name.lower().replace('-', '_')}"] = vals
# ββ Segment-level CATE summaries ββββββββββββββββββββββββββββββββββββββββββ
segment_cols = {
"zip_urban": "Urban",
"zip_suburban": "Suburban",
"zip_rural": "Rural",
"channel_web": "Web Channel",
"channel_phone": "Phone Channel",
"channel_multichannel": "Multichannel",
"newbie": "New Customer",
"mens": "Men's Buyer",
"womens": "Women's Buyer",
}
seg_summaries = {}
for col, label in segment_cols.items():
if col not in cate_df.columns:
continue
for val, grp_label in [(1, label), (0, f"Not {label}")]:
mask = cate_df[col] == val
if mask.sum() < 5:
continue
for model_key in ["t_learner", "x_learner", "causalforest"]:
col_name = f"cate_{model_key}"
if col_name not in cate_df.columns:
continue
seg_summaries.setdefault(model_key, []).append({
"segment": grp_label,
"n": int(mask.sum()),
"cate_mean": round(float(cate_df.loc[mask, col_name].mean()), 5),
"cate_std": round(float(cate_df.loc[mask, col_name].std()), 5),
"outcome_mean": round(float(cate_df.loc[mask, outcome_col].mean()), 4),
})
# ββ Overall ATE βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
overall = {}
for model_key in ["t_learner", "x_learner", "causalforest"]:
col_name = f"cate_{model_key}"
if col_name not in cate_df.columns:
continue
overall[model_key] = {
"ate_mean": round(float(cate_df[col_name].mean()), 5),
"ate_std": round(float(cate_df[col_name].std()), 5),
"pct_positive": round(float((cate_df[col_name] > 0).mean() * 100), 2),
}
# ββ Raw experiment ATE (naive difference in means) βββββββββββββββββββββββ
ctrl_outcome = cate_df.loc[cate_df["treatment"] == 0, outcome_col].mean()
trt_outcome = cate_df.loc[cate_df["treatment"] == 1, outcome_col].mean()
naive_ate = trt_outcome - ctrl_outcome
return {
"outcome": outcome_col,
"n_samples": len(cate_df),
"n_treated": int(T.sum()),
"n_control": int((1 - T).sum()),
"naive_ate": round(float(naive_ate), 5),
"overall_ate": overall,
"segment_summaries": seg_summaries,
# Top 10 and bottom 10 users by CausalForest CATE
"top10_causalforest": cate_df.nlargest(10, "cate_causalforest")[
available_feats + ["cate_causalforest"]
].round(4).to_dict("records"),
"bottom10_causalforest": cate_df.nsmallest(10, "cate_causalforest")[
available_feats + ["cate_causalforest"]
].round(4).to_dict("records"),
# Distribution for histogram
"causalforest_cates": cate_df["cate_causalforest"].round(5).tolist(),
"x_learner_cates": cate_df["cate_x_learner"].round(5).tolist(),
"t_learner_cates": cate_df["cate_t_learner"].round(5).tolist(),
}
def save_hte_results(results: dict, path: Path) -> None:
path.parent.mkdir(parents=True, exist_ok=True)
with open(path, "w") as f:
json.dump(results, f, indent=2, default=str)
def load_hte_results(path: Path) -> dict:
with open(path) as f:
return json.load(f)
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