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7277b21 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 | from __future__ import annotations
from dataclasses import dataclass
import numpy as np
from sklearn.linear_model import LogisticRegression, Ridge
from sklearn.model_selection import KFold
def sigmoid(values: np.ndarray) -> np.ndarray:
return 1.0 / (1.0 + np.exp(-np.clip(values, -30, 30)))
@dataclass(frozen=True)
class CausalSample:
x: np.ndarray
treatment: np.ndarray
outcome: np.ndarray
propensity: np.ndarray
y0: np.ndarray
y1: np.ndarray
ite: np.ndarray
@property
def ate(self) -> float:
return float(self.ite.mean())
def generate_scm(
samples: int,
seed: int,
confounding: float = 1.0,
noise: float = 1.0,
) -> CausalSample:
rng = np.random.default_rng(seed)
x = rng.normal(size=(samples, 3))
x1, x2, x3 = x.T
treatment_logit = -0.2 + confounding * (
1.05 * x1 - 0.85 * x2 + 0.60 * x1 * x2 + 0.45 * np.sin(x3)
)
propensity = np.clip(sigmoid(treatment_logit), 0.025, 0.975)
treatment = rng.binomial(1, propensity).astype(np.int8)
baseline = (
1.0
+ 1.35 * x1
+ 0.60 * x2
+ 0.75 * np.sin(x3)
+ 0.55 * x1 * x2
+ 0.30 * x3**2
)
ite = 2.0 + 0.50 * np.tanh(x1) - 0.35 * x2 + 0.20 * np.sin(x3)
disturbance = rng.normal(scale=noise, size=samples)
y0 = baseline + disturbance
y1 = baseline + ite + disturbance
outcome = np.where(treatment == 1, y1, y0)
return CausalSample(x, treatment, outcome, propensity, y0, y1, ite)
def nuisance_features(x: np.ndarray, correct: bool) -> np.ndarray:
if not correct:
return x.copy()
x1, x2, x3 = x.T
return np.column_stack(
[x1, x2, x3, x1 * x2, np.sin(x3), x3**2, np.tanh(x1)]
)
def fit_nuisance(
x: np.ndarray,
treatment: np.ndarray,
outcome: np.ndarray,
*,
propensity_correct: bool,
outcome_correct: bool,
) -> dict:
propensity_model = LogisticRegression(C=10.0, max_iter=1_000)
propensity_model.fit(nuisance_features(x, propensity_correct), treatment)
outcome_x = nuisance_features(x, outcome_correct)
control_model = Ridge(alpha=0.5).fit(
outcome_x[treatment == 0], outcome[treatment == 0]
)
treated_model = Ridge(alpha=0.5).fit(
outcome_x[treatment == 1], outcome[treatment == 1]
)
return {
"propensity": propensity_model,
"control": control_model,
"treated": treated_model,
"propensity_correct": propensity_correct,
"outcome_correct": outcome_correct,
}
def predict_nuisance(models: dict, x: np.ndarray) -> tuple[np.ndarray, ...]:
propensity = models["propensity"].predict_proba(
nuisance_features(x, models["propensity_correct"])
)[:, 1]
outcome_x = nuisance_features(x, models["outcome_correct"])
mu0 = models["control"].predict(outcome_x)
mu1 = models["treated"].predict(outcome_x)
return np.clip(propensity, 0.03, 0.97), mu0, mu1
def estimate_effects(
sample: CausalSample,
*,
propensity_correct: bool,
outcome_correct: bool,
folds: int = 5,
seed: int = 0,
) -> dict[str, float]:
n = len(sample.outcome)
propensity = np.zeros(n)
mu0 = np.zeros(n)
mu1 = np.zeros(n)
splitter = KFold(n_splits=folds, shuffle=True, random_state=seed)
for train, validation in splitter.split(sample.x):
models = fit_nuisance(
sample.x[train],
sample.treatment[train],
sample.outcome[train],
propensity_correct=propensity_correct,
outcome_correct=outcome_correct,
)
propensity[validation], mu0[validation], mu1[validation] = predict_nuisance(
models, sample.x[validation]
)
treatment = sample.treatment
outcome = sample.outcome
naive = outcome[treatment == 1].mean() - outcome[treatment == 0].mean()
treated_weighted = treatment * outcome / propensity
control_weighted = (1 - treatment) * outcome / (1 - propensity)
ipw = treated_weighted.mean() - control_weighted.mean()
outcome_regression = np.mean(mu1 - mu0)
influence = (
mu1
- mu0
+ treatment * (outcome - mu1) / propensity
- (1 - treatment) * (outcome - mu0) / (1 - propensity)
)
aipw = influence.mean()
standard_error = influence.std(ddof=1) / np.sqrt(n)
return {
"truth": sample.ate,
"naive": float(naive),
"ipw": float(ipw),
"outcome_regression": float(outcome_regression),
"aipw": float(aipw),
"aipw_standard_error": float(standard_error),
"aipw_ci_low": float(aipw - 1.96 * standard_error),
"aipw_ci_high": float(aipw + 1.96 * standard_error),
}
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